using the unit circle evaluate cos and sin for 30
23,973 results
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

Trig
Find sin(s+t) and (st) 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(st) =sin(s)cos(t)  cos(s)sin(t) =sin(3/5)cos(1/5)  cos(1/5)sin(3/5) =Sin3/5

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

Math
1. Write the expression as a function of an acute angle whose measure is less than 45. a. sin 80 b. sin (100) To find the postive acute angle, usually you would subtract 360 from the given measure. Would you have to subtract 45 from the given measure. 2.

Calculus AP
Evaluate the integral interval from [0 to pi] t sin(3t)dt Use integration by parts u=t and dv=sin(3t)dt. then du=dt and v=cos(3t)/3 here is my problem but Im having problem to solve with pi. ∫t sin(3t)dt = tcos(3t)/3  ∫[cos(3t)/3]dt =tcos(3t)/3 +

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

Trigonometry
Solve the equation for solutions in the interval 0

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?

Precalculus
Use one of the identities cos(t + 2πk) = cos t or sin(t + 2πk) = sin t to evaluate each expression. (Enter your answers in exact form.) (a) sin(19π/4) (b) sin(−19π/4) (c) cos(11π) (d) cos(53π/4) (e) tan(−3π/4) (f) cos(π/4) (g) sec(π/6+ 2π)

Mathematics
If x is an acute angle and tan x = 3/4 Evaluate : cos x  sin x cos x + sin x

PreCalc
Find the point (x, y) on the unit circle that corresponds to the real number 5pi/6. Use it to evaluate cos n. Is cos n = (sqrt(3)/2)?

maths
r1 and r2 are unit vectors in the xy plane making angles a and b with the positive xaxis.by considering r1.r2 derive cos(ab)=cos(a)cos(b)+sin(a)sin(b)

calc
Where do I start to prove this identity: sinx/cosx= 1cos2x/sin2x please help!! Hint: Fractions are evil. Get rid of them. Well, cos2x = cos2x  sin2x, so 1coscx = 1  cos2x  sin2x = 1  cos2x + sin2x You should be able to simplify this to 2*something

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(ab) = sin(a)cos(b)  cos(a)sin(b) Add the two equations:

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

Mathematics
if x is an acute angle and tan x 3/4 evaluate : cos x sin x /cos. x + sin x

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)

Calculous
Evaluate sin(theta) and cosine (theta) for the angle theta The graph gives you a point of (0.6,0.8) on the x y coordinate plane with a radius of what appears to be 1 ( unit circle ) sin (theta) = cos (theta) =

Math
use the sum and difference identities to find the cosine angle cos pi/9 cos pi/3  sin pi/9 sin pi/3 I do not know how to solve this because pi/9 is not on the unit circle.

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)

math
Evaluate. 1. sin^1(1/2) 2. cos^1[(root 3)/2] 3. arctan[(root3)/3] 4. cos(arccos2/3) 5. arcsin(sin 2pi) 6. sin(arccos 1)

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 ∫

s.g (math)
if a triangle with sides 12 unit and 5 unit is inscribed in a circle with BC as diameter, then find the value of sin square theta +cos square theta 1

Calculus
Find the velocity, v(t), for an object moving along the xaxis in the acceleration, a(t), is a(t)=cos(t)sin(t) and v(0)=3 a) v(t)=sin(t) + cos(t) +3 b) v(t)=sin(t) + cos(t) +2 c) v(t)= sin(t)  cos(t) +3 d) v(t)= sin(t)  cos(t) +4

Calculus
Find the velocity, v(t), for an object moving along the xaxis if the acceleration, a(t), is a(t) = cos(t) − sin(t) and v(0) = 3. a) v(t) = sin(t) + cos(t) +3 b) v(t) = sin(t) + cos(t) +2 c) v(t) = sin(t)  cos(t) +3 d) v(t) = sin(t)  cos(t) +4

trig
using the unit circle evaluate cos and sin for 30

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 +

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)

precal
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 

Trig
P(15/17,8/17) is found on the unit circle. Find sin theta and cos theta. P(15/17,8/17)= P(cos theta,sin theta) sin=8/17 cos=15/17

Math
use the unit circle to prove that tan(x/2) = (sin(x))/(1+cos(x))

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 +

trig
express 20sin theta + 4 cos theta as R sin(theta + alpha) R sin(theta + alpha) = R cos(alpha)sin(theta) + R sin(alpha)cos(theta) > Rcos(alpha) = 20 Rsin(alpha) = 4 The xy coordinates of a point on a circle of radius R that makes an angle og alpha with

calculus
We are not going to do that work for you, but will be glad to help you. The unit sphere is the sphere with radius 1 centered in the origin. They give you the coordinates of a vector. Compute the dot product of the vector and the local surface area normal

Mathematics
If x is an acute angle and tan x=3/4 evaluate cos x sin x÷ cos x+ sin x

Calculus
1.evaluate (integral sign)x cos 3x dx A.1/6 x^2 sin 3x + C B.1/3 x sin 3x 1/2 sin 3x +C C.1/3 x sin 3x +1/9 cos 3x +C

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

precalc
Find the exact value of each expression, if it exists: the 1 are representing the inverse functions! (a) sin 1 (√2/2) (b) cos−1 (−1) (c) sin( sin−1 (π)) (d) cos−1(cos(−4π/ 3)) (e) tan−1 (tan(0.6)) (f) cos−1(

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)

Trig.
tan^2BeatacscBetatan^2 (simplify) (sin/cos)^2Beta times 1/sin(sin/cos)^2 (sin^2/cos^2)(sin^2/cos^2)=sin/cos Is this correct?

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 +

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

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(14575) = sin

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. The part I am

trig
Let be an angle in standard position and the point (a, b) be the point of intersection of the terminal side of with the unit circle. State the unit circle definitions of the six trigonometric functions. cos = sec = sin = csc = tan = cot =

Integration?
Sorry, i have a load of questions on integration... thanks for any help provided! Evaluate the integrals: limit 0 to pi/4 ∫ [sec^2x]/[5+tanx] dx limit 0 to pi/6 ∫ [3cos3x]/[3+sin3x] dx limit 0 to 3 ∫ [2x1]/[x^2x+1] dx

Calculus
Evaluate ∫ (cos(x))^(1/2)sin(x)dx Let u = cos(x)? ∫ (u)^(1/2)sin(x)dx = ∫ [2u^(3/2)/3]sin(x)dx ∫ [2cos(x)^(3/2)/3] (cos(x)) dx? I thought this involved the FTC, but now I'm thinking that's false.

Math
Directions: Find the Location on Unit Circle, Period & General Solution for this problem>>>>>>> sin^2x=3cos^2x What I have so far: sin^2x=3cos^2 sin^2x/cos^2=3 tan^2x=3 tanx=+and sqrt3

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 +

math
I have a unit circle test tomorrow(converting sin csc cot tan sec cos of radians to numbers(ie cos (pi/4) == root2 over 2) what is a good way to study

math
Prove that for all real values of a, b, t (theta): (a * cos t + b * sin t)^2

Calculus
Evaluate the integral. S= integral sign I= absolute value S ((cos x)/(2 + sin x))dx Not sure if I'm doing this right: u= 2 + sin x du= 0 + cos x dx = S du/u = ln IuI + C = ln I 2 + sin x I + C = ln (2 + sin x) + C Another problem: S ((sin (ln x))/(x)) dx I

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

Math
Evaluate the integral of (e^2x)*sin^3 x dx I let u = e^2x, du = (1/2)e^2x dx v= (1/3)cos^3 x , dv =sin^3 x dx When I used integration by parts and solved it all out I got: (37/36)intgral of (e^2x)*sin^3 x dx = (1/3)(e^2x)*cos^3 x + (1/18)(e^2x)*sin^3 x

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

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)

trig integration
s integral endpoints are 0 and pi/2 i need to find the integral of sin^2 (2x) dx. i know that the answer is pi/4, but im not sure how to get to it. i know: s sin^2(2x)dx= 1/2 [1cos (4x)] dx, but then i'm confused. The indefinite integral of (1/2) [1cos

Precalc/Trig
evaluate the expression assuming that cos(x)=1/7, sin(y)=1/3, sin(u)=2/5 and cos(v)=1/3. what is cos(u+v)? sin(xy)? and tan(uv)?

math;)
Show that sin(x+pi)=sinx. So far, I used the sum formula for sin which is sin(a+b)=sin a cos b+cos a sin b. sin(x+pi)=sin x cos pi+cos x sin pi I think I am supposed to do this next, but I am not sure. sin(x+pi)=sin x cos x+sin pi cos pi If that is right

math
Evaluate. 1. sin^1(1/2) 2. cos^1[(root 3)/2] 3. arctan[(root3)/3] 4. cos(arccos2/3) 5. arcsin(sin 2pi) 6. sin(arccos 1) I got these values as my answers: 1. pi/6 2. 5pi/6 3. pi/6 4. 2/3 5. 2pi 6. 0 Can someone please tell me if they are right? thank

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)

Math
Solve this equation algebraically: (1sin 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.

Trigonometry (Help and Check)
Evaluate (exact answers): a) sin^1(cos30) Need help. What do I do? b) sin[(cos^1((sqrt2)/(2)))+[(sin^1((sqrt2)/(2)))] = sin(45+45) = sin90 = 1 Is this correct? c) cos(arctan5/7) = 7/(sqrt74) = (7sqrt74)/74 Is this correct? Please and Thank you!

Math
Evaluate the integral of 5^t * sin (5^t) *dt I started out with u = 5^t , but then I got stuck on du because I am not sure how to take the derivative of 5^t? The answer from the book is (1/ln5) cos(5^t) + C I understand the part with the antiderivative of

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)

trig
Find sin t,cos t and tan t when the terminal side of an angle of t radians passes through ( 3/5 , 4/5) on the unit circle.

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

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

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

Calculus repost
Does anybody know how to solve this question? a) Find the arc length function for the curve measured from the point P in the direction of increasing t from P and then reparametrize the curve with respect to arc length starting from P. b) Find the point 4

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)^(x1) * (sin x) =  x sin(x)cos^(x1)(x) (dy/dx)(dx/du)=

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)^(x1) * (sin x) =  x sin(x)cos^(x1)(x) (dy/dx)(dx/du)=

PreCalc
Evaluate the expression without using a calculator(show work please)? (sin pi/4 cos pi/6  sin pi/6 cos pi/4) the answer is 1/4(2ã3)

Mathematics
If x is acute angle, and tan x=3 , evaluate cos x−sin x _ __________ 4 cos x+sin x

K
(a) Find the indeﬁnite integrals of the following functions. (i) f (t) = 6 cos(3t) + 5e^−10t (ii) g(x) = 2112x^3/ x (x > 0) (iii) h(u) = cos^2( 1/8 u) (b) Evaluate: (this big F sign at the start, 5 at the top and 1 at the bottom) 5 1/4x (7 + 6x^2) dx

Calc
Find the exact total of the areas bounded by the following functions: f(x) = sinx g(x) = cosx x = 0 x = 2pi I set my calculator to graph on the xaxis as a 2pi scale. The two functions appear to cross three times between x = 0 and 2pi. (including 2pi) Now,

AP Calculus
Find the velocity, v(t), for an object moving along the xaxis if the acceleration, a(t), is a(t) = cos(t)  sin(t) and v(0) = 3 v(t) = sin(t) + cos(t) + 3 v(t) = sin(t) + cos(t) + 2 v(t) = sin(t)  cos(t) + 3 v(t) = sin(t)  cos(t) + 4

Calculus
Use the identity sin^2x+cos^2x=1 and the fact that sin^2x and cos^2x are mirror images in [0,pi/2], evaluate the integral from (0pi/2) of sin^2xdx. I know how to calculate the integral using another trig identity, but I'm confused about how to solve this

Calculus
Use the identity sin^2x+cos^2x=1 and the fact that sin^2x and cos^2x are mirror images in [0,pi/2], evaluate the integral from (0pi/2) of sin^2xdx. I know how to calculate the integral using another trig identity, but I'm confused about how to solve this

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(1sin x/cos x)=1 1/cos x + sin x/cos x(cos^2 x/cos x)=1 1+sin x/cos

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

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?

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)=pi2arctan(b) b=sin(pi2arctan(b)) Sub in Sin difference identity let 2U=(2arctan(b)) sin(ab)=sinacosbcosasinb

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)

Math
Show that for real x that {[cos x + 2 sin x + 1]/[cos x + sin x] } cannot have a value between 1 and 2. Let y = [(cos x+2 sin x + 1)/(cos x + sin x) ] y(cos x + sin x) = (cos x + 2 sin x + 1) sin x(y2) + cos x(y1)=1 , I just feel that this isn't the way

Inverse Functions & Trig. Equations
7. Evaluate sin[sin^1(1/2)]. a. 1/2 b. ð /6 c. 1/2 d.  ð /6 8. Evaluate cos[tan^1(5/12)]. a. 12/13 b. 12/5 c. 5/12 d. 5/13 9. Evaluate cos[sin^1(3/5)]. a. 4/5 b. 5/4 c. 4/5 d. 3/4

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

Calculus  MathMate Please help
ok, i tried to do what you told me but i cant solve it for c because they cancel each others out! the integral for the first one i got is [sin(c)cos(x)cos(c)sin(x)+sin(x)+c] and the integral for the 2nd one i got is [sin(c)cos(x)+cos(c)sin(x)sin(x)+c] I

Trigonometry
I need to prove that the following is true. Thanks. csc^2(A/2)=2secA/secA1 Right Side=(2/cosA)/(1/cosA  1) = (2/cosA)/[(1cosA)/cosA] =2/cosA x (cosA)/(1cosA) =2/(1cosA) now recall cos 2X = cos^2 X  sin^2 X and we could say cos A = cos^2 A/2  sin^2

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!

PreCalculus
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 tsin^4 t=12sin^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

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 π/6  sin^2 π/6 Is

Calculus
I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5(u^2))du I have a feeling I will be able to find the derivative easily,

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

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 3x1 c)12 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

Math (Trig)
I have a unit circle graph like the one at the top of a website (do a google search for 'unit circle trig functions' and click the second link, since I can't post links). I need to label the sine, cosine, tangent, secant, cosecant, and cotangent. I found

Maths
Determine the exact expression for the following.  cos(pi/4)=(x/60) I got x=60/√2 Is that correct? Also, I had a lot of trouble with this one: cos(pi/6)=(z/60) I got z=(√3 (60/√2))/2 That doesn't seem right, but I don'r know what I', doing wrong.

Trig!
The identities cos(ab)=cos(a)cos(b)sin(a)sin(b) and sin(ab)=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).

trig question
On a unit circle, sin x = square root 3 over 2, with center O. Vertical line from top to center of circle is PO. Horizontal line from middle to right of circle is OE. Another vertical line of AB is parallel to PO. And radius of circle (line from O to A) is

Calculus AP
hi again im really need help TextBook: James Stewart:Essential Calculus, page 311. Here the problem #27: First make a substitution and then use integration by parts to evaluate the integral. Integral from sqrt(pi/2) TO sqrt(pi)of θ^3 cos(θ^2)dθ. i did