Monday

January 23, 2017
Number of results: 133,100

**TRIG!**

Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 x = (sin^2x)^3 + (cos^2x)^3 = (sin^2x+cos...

*February 23, 2009 by hayden*

**tigonometry**

expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) Add the two equations: sin(a+b) + sin(a-b) = ...

*November 26, 2006 by Pablo*

**Mathematics - Trigonometric Identities**

Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y)(sin^2y) / (sin^...

*November 8, 2007 by Anonymous*

**algebra**

Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2 sin A I hope this will help. in my algebra ...

*February 18, 2007 by Valerie*

**trig**

Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity = sin(145-75) = sin 70 = cos 20 note that...

*November 26, 2006 by Paul C*

**math**

Can you please check my work. A particle is moving with the given data. Find the position of the particle. a(t) = cos(t) + sin(t) s(0) = 2 v(0) = 6 a(t) = cos(t) + sin(t) v(t) = sin(t) - cos(t) + C s(t) = -cos(t) - sin(t) + Cx + D 6 = v(0) = sin(0) -cos(0) + C C=7 2= s(0) = -...

*June 23, 2011 by Kay*

**math**

Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2 <= a^2 + b^2 I will be happy to critique your work. Start on the left, square it, (a * cos t + b * sin t)^2 = a^2 (1 - sin^2t) + 2ab sin t cost+ b^2 (1 - cos^2 t)= a^2 + b^2 - (a sin t - b cos t)^2...

*December 19, 2006 by mathstudent*

**Trig**

Find sin(s+t) and (s-t) if cos(s)= 1/5 and sin(t) = 3/5 and s and t are in quadrant 1. =Sin(s)cos(t) + Cos(s)Sin(t) =Sin(1/5)Cos(3/5) + Cos(-1/5)Sin(3/5) = 0.389418 Sin(s-t) =sin(s)cos(t) - cos(s)sin(t) =sin(-3/5)cos(1/5) - cos(1/5)sin(3/5) =Sin-3/5 cos-3/5 = -0.46602 HELP ...

*May 7, 2015 by Sally*

**Trig**

Given: cos u = 3/5; 0 < u < pi/2 cos v = 5/13; 3pi/2 < v < 2pi Find: sin (v + u) cos (v - u) tan (v + u) First compute or list the cosine and sine of both u and v. Then use the combination rules sin (v + u) = sin u cos v + cos v sin u. cos (v - u) = cos u cos v + ...

*December 29, 2006 by Nan*

**pre-cal**

Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48 cos^4 x + 18 cos^2 x - 1 I assume you are ...

*May 17, 2007 by ethan*

**math**

Given that sin x + sin y = a and cos x + cos y =a, where a not equal to 0, express sin x + cos x in terms of a. attemp: sin x = a - sin y cos x = a - cos y sin x + cos x = 2A - (sin y + cos y)

*November 21, 2015 by Chia LC*

**Calculus 12th grade (double check my work please)**

1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with respect to x. A.-sin (2x) B.-2x sin (x^2...

*March 6, 2011 by anon*

**Precal**

I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 = - sin^6 A - cos^6 A + 2sin^3 A cos^3 A - 2sin^3 ...

*January 14, 2010 by Joe*

**trig**

The expression 4 sin x cos x is equivalent to which of the following? (Note: sin (x+y) = sin x cos y + cos x sin y) F. 2 sin 2x G. 2 cos 2x H. 2 sin 4x J. 8 sin 2x K. 8 cos 2x Can someone please explain how to do this problem to me?

*June 12, 2009 by B.S.*

**Calc.**

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...

*March 9, 2011 by Chelsea*

**calculus**

Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1...

*March 10, 2011 by Chelsea*

**Trigonometry**

Solve the equation for solutions in the interval 0<=theta<2pi Problem 1. 3cot^2-4csc=1 My attempt: 3(cos^2/sin^2)-4/sin=1 3(cos^2/sin^2) - 4sin/sin^2 = 1 3cos^2 -4sin =sin^2 3cos^2-(1-cos^2) =4sin 4cos^2 -1 =4sin Cos^2 - sin=1/4 (1-sin^2) - sin =1/4 -Sin^2 - sin =-3/4 ...

*March 7, 2016 by Renee*

**Math**

Solve this equation algebraically: (1-sin x)/cos x = cos x/(1+sin x) --- I know the answer is an identity, and when graphed, it looks like cot x. I just don't know how to get there. I tried multiplying each side by its conjugate, but I still feel stuck. This is what I have so ...

*October 18, 2009 by Momo*

**math**

how would you prove that sin^2(a)-cos^2(b)= sin^2(b)-cos^2(a). i'm not completely sure that this is right but i used the difference of two squares on it to get (sin(a)+cos(b))(sin(a)-cos(b)) then after that i am stuck. please help

*April 6, 2009 by mike*

**trig**

it says to verify the following identity, working only on one side: cotx+tanx=cscx*secx Work the left side. cot x + tan x = cos x/sin x + sin x/cos x = (cos^2 x +sin^2x)/(sin x cos x) = 1/(sin x cos x) = 1/sin x * 1/cos x You're almost there. thanks so much! i could not figure...

*May 7, 2007 by Devon*

**Math(Please check)**

Use the fundamental identities to simplify the expression. tan^2 Q / sec^2 Q sin^2/cos^2 / 1/cos^2 = sin^2 / cos^2 times cos^2 / 1 = The cos^2 cancels out so sin^2 is left. Is this correct?

*March 5, 2010 by Hannah*

**Math Help Please**

What are the ratios for sin A and cos A? The diagram is not drawn to scale. Triangle Description- AB = 29 AC = 20 BC - 21 A. sin A = 20/29, cos A = 21/29 B. sin A = 21/29, cos A = 20/21 C. sin A = 21/29, cos A = 20/29****? D. sin A = 21/20, cos A = 20/21 Please help and explain!

*June 7, 2016 by Battia Anne*

**Math**

the original problem was: (sin x + cos x)^2 + (sin x - cos x)^2 = 2 steps too please I got 1 for (sin x + cos x)^2 but then what does (sin x - cos x)^2 become since it's minus?

*March 19, 2011 by Amy*

**math**

Proving Trigonometric Identities 1. sec^2x + csc^2x= (sec^2 x)(csc^2 x) 2. sin ^3 x / sin x - cos 3x / cos x = 2 3. 1- cos x/ sin x= sin x/ 1+ cos x 4. 2 sin x cos ^2 (x/2)- 1/x sin (2x) = sinx 5. cos 2 x + sin x/ 1- sin x= 1+ 2 sin x

*March 20, 2013 by mm*

**Math**

Prove each identity: a) 1-cos^2x=tan^2xcos^2x b) cos^2x + 2sin^2x-1 = sin^2x I also tried a question on my own: tan^2x = (1 – cos^2x)/cos^2x R.S.= sin^2x/cos^2x I know that the Pythagorean for that is sin^2x + cos^2x That's all I could do.

*July 18, 2011 by Kate*

**Math**

State the restrictions on the variables for these trigonometric identities. a)(1 + 2 sin x cos x)/ (sin x + cos x) = sin x + cos x b) sin x /(1+ cos x) = csc x - cot x

*December 22, 2010 by Emily*

**Math (Linear Systems)**

28 N + T2 sin 12 = T1 sin 42 T2 cos 12 = T1 cos 42 T2 sin 12 + T3 sin 54 = W2 T2 cos 12 = T3 cos 54 Im solving for T1,2,3 and W2 I just cant seem to get the system to work

*September 29, 2012 by Joe Rogers*

**Integral**

That's the same as the integral of sin^2 x dx. Use integration by parts. Let sin x = u and sin x dx = dv v = -cos x du = cos x dx The integral is u v - integral of v du = -sinx cosx + integral of cos^2 dx which can be rewritten integral of sin^2 x = -sinx cos x + integral of (...

*February 20, 2007 by drwls*

**Trigonometry**

Does anyone have a good website that shows the proofs for these equations? sin(u+v) = sin(u)cos(v) + sin(v)cos(u) cos(u+v) = cos(u)cos(v) + sin(v)sin(u) Thanks!

*December 16, 2008 by Karth*

**Trigonometry**

Please review and tell me if i did something wrong. Find the following functions correct to five decimal places: a. sin 22degrees 43' b. cos 44degrees 56' c. sin 49degrees 17' d. tan 11degrees 37' e. sin 79degrees 23'30' f. cot 19degrees 0' 25'' g. tan 64degrees 6' 45'' h. cos...

*January 1, 2011 by Anon*

**Math, Pre-Calc**

the original problem was: Solve: sin(3x)-sin(x)=cos(2x) so far i've gooten to: sin(x)(2sin(x)cos(x)-1)=cos^2(x)-sin^2(x) Where would I go from here?

*April 23, 2009 by Katie*

**Geometry One multiple choice question!**

Write the ratios for sin A and cos A. {picture is of a right triangle, ABC. segment AC is 8, segment AB is 17, and segment CB is 15.} sin A=15/17, cos A=8/17 sin A=15/8, cos A=8/17 sin A=15/17, cos A=8/15 sin A=8/17, cos A=15/17

*May 29, 2012 by LEXI*

**Geometry Please Help With One Multiple Choice**

Write the ratios for sin A and cos A. {picture is of a right triangle, ABC. segment AC is 8, segment AB is 17, and segment CB is 15.} sin A=15/17, cos A=8/17 sin A=15/8, cos A=8/17 sin A=15/17, cos A=8/15 sin A=8/17, cos A=15/17

*May 29, 2012 by LEXI*

**Math**

the original problem was: Solve: sin(3x)-sin(x)=cos(2x) so far i've gotten to: sin(x)(2sin(x)cos(x)-1)=cos^2(x)-sin^2(x) Where would I go from here?

*April 23, 2009 by Katie*

**MATH**

Hi, I really need help with these questions. I did some of them halfway, but then I got stuck. Would you please help me? Thank you so much. Prove the identity.... 1. sec x + tan x(1-sin x/cos x)=1 1/cos x + sin x/cos x(cos^2 x/cos x)=1 1+sin x/cos x(cos^2x/cos x)=1 I got stuck...

*January 2, 2014 by LIZZIE010*

**Precalc**

Let x, y, and z be real numbers such that cos(x) + cos(y) + cos(z) = sin(x) + sin(y) + sin(z) = 0. Prove that cos(2x) + cos(2y) + cos(2z) = sin(2x) + sin(2y) + sin(2z) = 0.

*May 6, 2016 by Pip*

**math**

Eliminate the parameter (What does that mean?) and write a rectangular equation for (could it be [t^2 + 3][2t]?) x= t^2 + 3 y = 2t Without a calculator (how can I do that?), determine the exact value of each expression. cos(Sin^-1 1/2) Sin^-1 (sin 7pi/6) x= t^2 + 3 y = 2t ...

*August 3, 2007 by Anonymous*

**precalculus**

For each of the following determine whether or not it is an identity and prove your result. a. cos(x)sec(x)-sin^2(x)=cos^2(x) b. tan(x+(pi/4))= (tan(x)+1)/(1-tan(x)) c. (cos(x+y))/(cos(x-y))= (1-tan(x)tan(y))/(1+tan(x)tan(y)) d. (tan(x)+sin(x))/(1+cos(x))=tan(x) e. (sin(x-y...

*April 14, 2013 by anonymous*

**Math(Please help)**

1)tan Q = -3/4 Find cosQ -3^2 + 4^2 = x^2 9+16 = sqrt 25 = 5 cos = ad/hy = -4/5 Am I correct? 2) Use the sum and difference identites sin[x + pi/4] + sin[x-pi/4] = -1 sinx cospi/4 + cosxsin pi/4 + sinx cos pi/4 - cosx sin pi/4 = -1 2 sin x cos pi/4 =-1 cos pi/4 = sqr2/2 2sin^x...

*March 16, 2010 by Abbey*

**Trigonometry**

I need help with I just can't seem to get anywhere. this is as far as I have got: Solve for b arcsin(b)+ 2arctan(b)=pi arcsin(b)=pi-2arctan(b) b=sin(pi-2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b)) sin(a-b)=sinacosb-cosasinb =(sin(pi))(cos(2U))-(cos(pi))(sin(...

*July 27, 2007 by Jen*

**Trig!**

The identities cos(a-b)=cos(a)cos(b)sin(a)sin(b) and sin(a-b)=sin(a)cos(b)-cos(a)sin(b) are occasionally useful. Justify them. One method is to use rotation matricies. Another method is to use the established identities for cos(a+b) and sin (a+b).

*September 27, 2011 by Elle*

**Trig**

If angle A is 45 degrees and angle B is 60 degrees. Find sin(A)cos(B), find cos(A)sin(B), find sin(A)sin(B), and find cos(A)cos(B) The choises for the first are: A. 1/2[sin(105)+sin(345)] B. 1/2[sin(105)-sin(345)] C. 1/2[sin(345)+cos(105)] D. 1/2[sin(345)-cos(105)] You don't ...

*October 8, 2016 by Sade*

**Math - Calculus**

The identity below is significant because it relates 3 different kinds of products: a cross product and a dot product of 2 vectors on the left side, and the product of 2 real numbers on the right side. Prove the identity below. | a × b |² + (a • b)² = |a|²|b|² My work, ...

*March 3, 2008 by Anonymous*

**Math - Solving Trig Equations**

What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x)) = 4cos^4(x) - 4cos^2(x) + 1 5cos^4(x) - 5cos^...

*November 24, 2007 by Anonymous*

**math**

find all solutions in the interval [0,2 pi) sin(x+(3.14/3) + sin(x- 3.14/3) =1 sin^4 x cos^2 x Since sin (a+b) = sina cosb + cosb sina and sin (a-b) = sina cosb - cosb sina, the first problem can be written 2 sin x cos (pi/3)= sin x The solution to sin x = 1 is x = pi/2 For ...

*March 22, 2007 by lauren*

**Trig.**

tan^2BeatacscBeta-tan^2 (simplify) (sin/cos)^2Beta times 1/sin-(sin/cos)^2 (sin^2/cos^2)-(sin^2/cos^2)=-sin/cos Is this correct?

*January 10, 2010 by Tara*

**Math(Please help)**

2) Use the sum and difference identites sin[x + pi/4] + sin[x-pi/4] = -1 sinx cospi/4 + cosxsin pi/4 + sinx cos pi/4 - cosx sin pi/4 = -1 2 sin x cos pi/4 =-1 cos pi/4 = sqr2/2 2sin^x(sqrt2/2) = -1 sin x = -sqrt2 x = 7pi/4 and 5pi/4 Am I correct?

*March 17, 2010 by Abbey*

**precalc**

prove the identity: cos^4 - sin^4 = cos^2 - sin^2 (cos^2 + sin^2)(cos^2 - sin^2) cos^2 + sin^2 = 1 cos^2 - sin^2 = cos^2 - sin^2 is this correct?

*October 14, 2015 by dipper*

**maths**

Choose the option that gives an expression for the indefinite integral ʃ (cos(4x) + 2x^2)(sin(4x) − x) dx. In each option, c is an arbitrary constant. Options A cos(4x) + 2x^2 +c B -1/8cos(4x) + 2x^2)^2 +c C 1/4 (sin(4x) − x)^2 + c D (1/(2 (sin(4x) − x...

*May 11, 2011 by albert*

**Pre-Calculus**

I don't understand,please be clear! Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x 4. sin^3 z cos^2 z= sin^3 z - sin^5 z

*October 31, 2013 by Anonymous*

**Precalculus with Trigonometry**

Prove or disprove the following Identities: cos(-x) - sin(-x) = cos(x) + sin (x) sin raised to the 4 (theta) - cos raised to the 4 (theta) = sin squared (theta) - cos squared (theta) cos (x+(pi)/(6)) + sin (x - (pi)/(3)) = 0 cos(x+y)cos(x-y) = cos squared (x) - sin squared (y...

*April 4, 2013 by Natalie*

**trigonometry (please double check this)**

Solve the following trig equations. give all the positive values of the angle between 0 degrees and 360 degrees that will satisfy each. give any approximate value to the nearest minute only. 1. sin2ƒÆ = (sqrt 3)/2 2. sin^2ƒÆ = cos^2ƒÆ + 1/2 3. sin 2x - cosx = 0 4. cos 4x...

*March 3, 2011 by anon*

**Trig**

sin^4t-cos^4t/sin^2t cos^2t= sec^2t-csc^2t i have =(sin^2t+cos^2t)(sin^2t+cos^2t)/sin^2tcos^2t then do i go =(sin^2t+cos^2t)/sin^2tcos^2t stumped

*April 19, 2012 by Josh*

**add math**

Given sin (x-y)=1/4, sin x cos y=3/5,and tan y=3/2,without using mathematical table or scientific calculator,find the values for: (a)cos x sin y (b)cos (x+y)

*June 24, 2011 by cianhuan*

**pre calc trig check my work please**

sin x + cos x -------------- = ? sin x sin x cos x ----- + ----- = sin x sin x cos x/sin x = cot x this is what i got, the problem is we have a match the expression to the equation work sheet and this is not one of the answers. need to figure out what im doing wrong so i can ...

*October 20, 2010 by Anna*

**maths**

Choose the two options which are true for all values of x 1) cos (x) = cos ( x – pie/2) 2) sin (x + pie/2) = cos (x – pie/2) 3) cos (x) = sin (x – pie/2) 4) sin (x) = sin (x + 4pie) 5) sin (x) = cos (x – pie/2) 6) sin^2 (x) + cos^2 (x) = pie would it be 1 and 3 ?? I ...

*April 22, 2007 by katie*

**Pre-Calculus**

Prove that each equation is an identity. I tried to do the problems, but I am stuck. 1. cos^4 t-sin^4 t=1-2sin^2 t 2. 1/cos s= csc^2 s - csc s cot s 3. (cos x/ sec x -1)- (cos x/ tan^2x)=cot^2 x 4. sin^3 z cos^2 z= sin^3 z - sin^5 z

*October 31, 2013 by Anonymous*

**Math**

3. find the four angles that define the fourth root of z1=1+ sqrt3*i z = 2 * (1/2 + i * sqrt(3)/2) z = 2 * (cos(pi/3 + 2pi * k) + i * sin(pi/3 + 2pi * k)) z = 2 * (cos((pi/3) * (1 + 6k)) + i * sin((pi/3) * (1 + 6k))) z^(1/4) = 2^(1/4) * (cos((pi/12) * (1 + 6k)) + i * sin((pi/...

*January 28, 2014 by Anonymous*

**Math-Trigonometry**

Show that if x, y, and z are consecutive terms of an arithmetic sequence, and tan y is defined, then (sin x + sin y + sin z) / (cos x + cos y + cos z) = tan y. So I tried letting x = y-k (since x,y,z are consecutive terms of an arithmetic sequence), then z= y+k So we get (sin(...

*November 7, 2013 by Sam*

**calculus**

Find the points on the curve y= (cos x)/(2 + sin x) at which the tangent is horizontal. I am not sure, but would I find the derivative first: y'= [(2 + sin x)(-sin x) - (cos x)(cos x)]/(2 + sin x)^2 But then I don't know what to do or if that is even correct??? Would I ...

*October 24, 2010 by CMM*

**math**

Express the following in simplest form: (complex fraction) Sin(x) - Cos(x) Cos(x) Sin(x) _______________ 1 - 1 Cos(x) Sin(x)

*February 26, 2010 by nellie*

**precalculus**

I don't understand this problem: (Tanө + cos ө)/ (sec ө + cot ө) so I start off like this: ={(sinө / cos ө)+cosө}{cos ө + (sinө/cosө)} =[(sin ө +cos^2ө) (cos^2ө +sin ө)]/ cos ө but what ...

*February 22, 2009 by allison*

**math**

A trigonmetric polynomial of order n is t(x) = c0 + c1 * cos x + c2 * cos 2x + ... + cn * cos nx + d1 * sin x + d2 * sin 2x + ... + dn * sin nx The output vector space of such a function has the vector basis: { 1, cos x, cos 2x, ..., cos nx, sin x, sin 2x, ..., sin nx } Use ...

*January 16, 2008 by mathstudent*

**verifying trigonometric identities**

How do I do these problems? Verify the identity. a= alpha, b=beta, t= theta 1. (1 + sin a) (1 - sin a)= cos^2a 2. cos^2b - sin^2b = 2cos^2b - 1 3. sin^2a - sin^4a = cos^2a - cos^4a 4. (csc^2 t / cot t) = csc t sec t 5. (cot^2 t / csc t) = csc t = sin t

*March 3, 2008 by Anonymous*

**trigonometry HELP pleasE!**

these must be written as a single trig expression, in the form sin ax or cos bx. a)2 sin 4x cos4x b)2 cos^2 3x-1 c)1-2 sin^2 4x I need to learn this!! if you can show me the steps and solve it so I can learn I'd be grateful!!! 1) apply the formula for sin 2z 2)3) cos^2z + sin^...

*November 1, 2006 by jim*

**Mathematics - Trigonometric Identities**

Prove: sin^2x - sin^4x = cos^2x - cos^4x What I have, LS = (sinx - sin^2x) (sinx + sin^2x) = (sinx - 1 -cos^2x) (sinx + 1 - cos^2x) = sin^2x + sinx - sinx - cos^2xsinx - cos^2xsinx - 1 - 1 + cos^4x = sin^2x - 2cos^2xsinx - 2 + cos^4x Where did I go wrong? Can anyone please ...

*November 9, 2007 by Anonymous*

**trigonometry**

find without tables or calculator. (1) sin^2 (22 1/2)- cos^2 (22 1/2) (2) sin 60 cos 30 + sin 30 cos 60 (3) cos(90-y) = sin 56degree 47^i

*July 26, 2008 by matrixxavier*

**Math (trigonometric identities)**

I was given 21 questions for homework and I can't get the last few no matter how hard and how many times I try. 17. Sinx-1/sinx+1 = -cos^2x/(sinx+1)^2 18. Sin^4x + 2sin^2xcos^2x + cos^4x = 1 19. 4/cos^2x - 5 = 4tan^2x - 1 20. Cosx - sinx - cos^3x/Cosx = sin^2 - tanx 21. Sin^2x...

*December 4, 2012 by Kim*

**Trigonometry**

I need to prove that the following is true. Thanks. csc^2(A/2)=2secA/secA-1 Right Side=(2/cosA)/(1/cosA - 1) = (2/cosA)/[(1-cosA)/cosA] =2/cosA x (cosA)/(1-cosA) =2/(1-cosA) now recall cos 2X = cos^2 X - sin^2 X and we could say cos A = cos^2 A/2 - sin^2 A/2 and of course sin^...

*April 17, 2007 by Dirk*

**Math**

Show using integration by parts that: e^3x sin(2x)dx = 4/26 e^3x (3/2 sin(2x) - cos(2x)) +c Bit stuck on this. Using rule f udv = uv - f vdu u = e^3x dv + sin(2x)dx f dv = v du/dx = 3e^3x v = -1/2 cos(2x) so uv - f vdu: = (e^3x)(-1/2 cos(2x)) - (-1/2 cos(2x))(3e^3x) Don't know...

*March 24, 2016 by Danny*

**Mathematics - Trigonometric Identities - Reiny**

Mathematics - Trigonometric Identities - Reiny, Friday, November 9, 2007 at 10:30pm (sinx - 1 -cos^2x) (sinx + 1 - cos^2x) should have been (sinx - 1 + cos^2x) (sinx + 1 - cos^2x) and then the next line should be sin^2x + sinx - cos^2xsinx - sinx - 1 + cos^2 x + cos^2xsinx - ...

*November 10, 2007 by Anonymous*

**math**

Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a cos b- sina sin b? or is it something different. When plugging it in the calculator, do we enter it with cos and then the (cos^-1(19 pi)).

*April 14, 2012 by Anonymous*

**MATH...THE GRAPHS OF SINE, COSINE AND TANGENT**

anyone explain how this cos 2A cos A – sin 2A sin A can become to this cos (2A + A) = cos 3A

*January 21, 2011 by mie_y98*

**calculus**

Find complete length of curve r=a sin^3(theta/3). I have gone thus- (theta written as t) r^2= a^2 sin^6 t/3 and (dr/dt)^2=a^2 sin^4(t/3)cos^2(t/3) s=Int Sqrt[a^2 sin^6 t/3+a^2 sin^4(t/3)cos^2(t/3)]dt =a Int Sqrt[sin^4(t/3){(sin^2(t/3)+cos^2(t/3)}]dt=a Int Sqrt[sin^4(t/3)dt =a ...

*September 18, 2013 by ms*

**Math**

Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve. x = sec Q y = cos Q x^2 + y^2 = 1/cos^2 + sin^2/cos^2 = x^2(1 +sin^2) = x^2(2-cos^2) x^2(2-1/x^2) = 2x^2 - 1 x^2 - y^2 = 1 My teacher said to use secant*cosine = 1. ...

*May 4, 2010 by Abbey*

**math**

How would you establish this identity: (1+sec(beta))/(sec(beta))=(sin^2(beta))/(1-cos(beta)) on the right, sin^2 = 1-cos^2, that factor to 1-cos * `1+cos, then the denominator makes the entire right side 1+cosB which is 1+1/sec which is 1/sec (sec+1) qed using sec(beta) = 1/...

*June 13, 2007 by michelle*

**Trig Help!**

Question: Trying to find cos π/12, if cos π/6 = square root 3 over 2, how to find cos π/12 using DOUBLE angle formula? This is what I got so far.. cos 2(π/6) = cos (π/6 + π/6) = (cos π/6)(cos π/6) - (sin π/6)(sin π/6) = cos^2...

*April 27, 2012 by Anonymous*

**Limit Calculas**

Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am not sure the next steps. Can someone help me? 1. sin(2y)/(sin(5y)*cos(5y)) 2. (sin(2y)*cos(5y))/sin(5y)

*September 12, 2012 by Ryan*

**calculus**

Evaluate lim->4 sin(2y)/tan(5y) Here is what I have so far. I am not sure the next steps. Can someone help me? 1. sin(2y)/(sin(5y)*cos(5y)) 2. (sin(2y)*cos(5y))/sin(5y)

*September 12, 2012 by Ryan*

**Pre-Calc**

How do I solve this? My work has led me to a dead end. tan(45-x) + cot(45-x) =4 my work: (tan45 - tanx)/(1+ tan45tanx) + (cot45 - cotx)/(1 + cot45cotx) = 4 (1-tanx)/(1+tanx) + (1-cotx)/(1+cotx) = 4 Then I found a common denominator, giving me this: (2-2cotxtanx)/(1+cotx+tanx+...

*February 7, 2007 by Jess*

**math**

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of si -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the special tables sin(ƒÎ/6) = cos(ƒÎ/3) = 1/...

*August 24, 2011 by jenny*

**math**

Use the exact values of the sin, cos and tan of pi/3 and pi/6, and the symmetry of the graphs of sin, cos and tan, to find the exact values of sin -pi/6, cos 5/3pi and tan 4pi/3. I have found the answers to the first three using the special tables sin pi/6 = cos pi/3 = 1/2 cos...

*August 25, 2011 by jenny*

**Math**

verify the following identity used in calculus: cos(x+h)-cos(x)/h=cos(x)[cos(h)-1/h]-sin(x)[sin(h)/h]

*May 2, 2011 by Monica Mosher*

**Trig**

Solve in terms of sine and cosine: sec(x) csc(x)- sec(x) sin(x) so far I have: 1/cos(x) 1/sin(x) - 1/cos(x) sin(x) I am not sure where to go to from there. The book says the answer is cot(x) or cos(x)/sin(x) Thank you in advance.

*April 9, 2008 by Dennis*

**Trigonometry desperate help, clueless girl here**

2. solve cos 2x-3sin x cos 2x=0 for the principal values to two decimal places. 3. solve tan^2 + tan x-1= 0 for the principal values to two decimal places. 4. Prove that tan^2(x) -1 + cos^2(x) = tan^2(x) sin^2 (x). 5.Prove that tan(x) sin(x) + cos(x)= sec(x) 6.Prove that tan(x...

*August 16, 2013 by Suzy*

**Trigonometry**

1.Solve tan^2x + tan x – 1 = 0 for the principal value(s) to two decimal places. 6.Prove that tan y cos^2 y + sin^2y/sin y = cos y + sin y 10.Prove that 1+tanθ/1-tanθ = sec^2θ+2tanθ/1-tan^2θ 17.Prove that sin^2w-cos^2w/tan w sin w + cos w tan w = ...

*January 1, 2013 by Alonso*

**Math, derivatives**

Let g(x) = sin (cos x^3) Find g ' (x): The choices are a) -3x^2sinx^3cos(cos x^3) b) -3x^2sinx^3sin(cos x^3) c) -3x^2cosx^3sin(cos x^3) d) 3x^2sin^2(cos x^3) I'm not exactly sure where I should start. Should I begin with d/dx of sin? Or do the inside derivative first...and do ...

*May 11, 2008 by Marissa*

**Math - Solving for Trig Equations**

Solve the following equation for 0 less than and/or equal to "x" less than and/or equal to 360 -- cos^2x - 1 = sin^2x -- Attempt: cos^2x - 1 - sin^2x = 0 cos^2x - 1 - (1 - cos^2x) = 0 cos^2x - 1 - 1 + cos^2x = 0 2cos^2x - 2 = 0 (2cos^2x/2)= (-2/2) cos^2x = -1 cosx = square ...

*November 22, 2007 by Anonymous*

**Calculus**

Integrate 1/sinx dx using the identity sinx=2(sin(x/2)cos(x/2)). I rewrote the integral to 1/2 ∫ 1/(sin(x/2)cos(x/2))dx, but I don't know how to continue. Thanks for the help. Calculus - Steve, Tuesday, January 12, 2016 at 12:45am 1/2 ∫ 1/(sin(x/2)cos(x/2))dx let u...

*January 12, 2016 by Andre-Steve, please reply*

**Cos-Derivative**

y= (cos^3 x) (cos 3x) I got -3 sin(3x) cos^3x - 3 sin(x) cos (3x) cos^2 (x) using the product rule Is this right? Thanks.

*March 14, 2013 by Mark*

**Pre Calculus**

Use one of the identities cos(t + 2ðk) = cos t or sin(t + 2ðk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(17ð/4) (b) sin(−17ð/4) (c) cos(17ð) (d) cos(45ð/4) (e) tan(−3ð/4) (f) cos(7ð/4) (g) sec(ð/6+2ð) (h) csc(2ð &#...

*March 10, 2012 by Stephanie823*

**Pre Calculus**

Use one of the identities cos(t + 2ðk) = cos t or sin(t + 2ðk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(17ð/4) (b) sin(−17ð/4) (c) cos(17ð) (d) cos(45ð/4) (e) tan(−3ð/4) (f) cos(7ð/4) (g) sec(ð/6+2ð) (h) csc(2ð &#...

*March 10, 2012 by Stephanie823*

**Math**

Which of the following are inverse functions? 1. Arcsin x and sin x 2. cos^-1 x and cos x 3. csc x and sin x 4. e^x and ln x 5. x^2 and +/- sqrt x 6. x^3 and cubic root of x 7. cot x and tan x 8. sin x and cos x 9. log x/3 and 3^x I believe the answers are 2, 4, 6, and 9, but ...

*April 16, 2009 by Anonymous*

**math (repost)**

Which of the following are inverse functions? 1. Arcsin x and sin x 2. cos^-1 x and cos x 3. csc x and sin x 4. e^x and ln x 5. x^2 and +/- sqrt x 6. x^3 and cubic root of x 7. cot x and tan x 8. sin x and cos x 9. log x/3 and 3^x I believe the answers are 2, 4, 6, and 9, but ...

*April 16, 2009 by Anonymous*

**Math (Trig)**

sorry, another I can't figure out Show that (1-cot^2x)/(tan^2x-1)=cot^2x I started by factoring both as difference of squares. Would I be better served by writing in terms of sine and cosine? Such as: [1-(cos^2x/sin^2x)]/[(sin^2x/cos^2x)-1]=(cos^2x/sin^2x)

*April 9, 2008 by mtd*

**Trig**

Simplify sin x cos^2x-sinx Here's my book's explanation which I don't totally follow sin x cos^2x-sinx=sinx(cos^2x-1) =-sinx(1-cos^2x) =-sinx(sin^2x) (Where does sine come from and what happend to cosine?) =-sin^3x

*January 4, 2010 by Tara*

**Math**

Evaluate *Note - We have to find the exact value of these. That I know to do. For example sin5π/12 will be broken into sin (π/6) + (π/4) So... sin 5π/12 sin (π/6) + (π/4) sin π/6 cos π/4 + cos π/6 sin π/4 I get all those steps...

*November 25, 2007 by Anonymous*

**Trigonometry**

For 0<x<pi/2, sin x and cos x are both less than 1 and greater than 0 (easy to see). We are also given that sin^2x+cos^2x=1. Use this to show that sin^7x+cos^7x<1 for 0<x<pi/2. Unsure on how to proceed?

*October 27, 2013 by Sam*

**Integration by Parts**

integral from 0 to 2pi of isin(t)e^(it)dt. I know my answer should be -pi. **I pull i out because it is a constant. My work: let u=e^(it) du=ie^(it)dt dv=sin(t) v=-cos(t) i integral sin(t)e^(it)dt= -e^(it)cos(t)+i*integral cost(t)e^(it)dt do integration by parts again, then I ...

*April 16, 2015 by Ashley*

**MathsSs triG**

Consider sin(x-360)sin(90-x)tan(-x)/cos(90+x) 1.A.SIMPLIFY sin(x-360)sin(90-x)tan(-x)/cos(90+x) to a single trigonometric ratio B.hence or otherwise without using a calculator,solve for X if 0<X<360. sin(x-360)sin(90-x)tan(-x)/cos(90+x) =0,5 2.A.prove that 8/sin^2A - 4/1...

*October 3, 2013 by katlego ratsoma*