A and B are positive acute angles. if sin A=4/5 and cos B=8/17 find the value of tan (AB) is the answer =43/100
105,281 results
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

Geometry
For the acute angles in a right triangle, sin (4x)° = cos (3x + 13) °. What is the number of degrees in the measure of the smaller angle

trig
A and B are positive acute angles. if sin A=4/5 and cos B=8/17 find the value of tan (AB) is the answer =43/100

Math
If A and B are acute angle such that SinA=8/17 and CosB=3/5.Find 1, Cos(A+B) 2, Sin(A+B) 3, Sin(AB)

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 +

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 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

ALGEBRA 1
If x and 3x10 represent the measure of the acute angles of a right tringle find the value of x. THANKS Let's take it step by step. A triangle has 3 angles in it. Those three angles, when added together, is 180. In a right triangle, one of the angles is 90

Maths
if COS A=3/5 and Sin B=7/25, when A us acute and B is obtuse, find without using tables. the value of COS(A+B)

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)

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.

Trigonometry
find (acute) angle A, given: a. sin A = 0.4919 b. tan A = 2.7775 c. cos A = 0.5757

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)

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

geometry
Find the measure of the acute angle x, if : sin(x)=0.0175; sin(x)=0.5015; cos(x)=0.06814; cos(x)=0.0670. I know that Sin(x)=opp./hyp. and that cos(x)=adj./hyp. but i have no clue about how to find the xs in these equations

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

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

math
1. express tan 11pi/6 in terms of a positive acute angle 2. solve for x : sin(4x7) = cos 17 thank you!

maths (trigonometry)
sin(alphabita)=1/2 and cos(alpha+bita)=1/2, where alpha and bita are positive acute angles then what is the value of alpha and bita

math (trig)
i have some problems doing trig the first one is: Show that cos(x/2) sin(3x/2) = ½(sinx + sin2x) i know that you are supposed to substitute all those trig function things in it but i kind of forgot how to the only that i can see substituting in is the

geometry
which of the following statements are true? a. if two angles form a linear pair, then the angles are supplementary b. if two angles are right angles, then the angles are complementary c. if two angles have the same measure, then the angles are congruent.

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?

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

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

Trigonometry
Solve the equation for solutions in the interval 0

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.

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 ∫

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/1tanθ = sec^2θ+2tanθ/1tan^2θ 17.Prove that sin^2wcos^2w/tan w sin w + cos w tan w =

pleeaasee hellpp!!
A and B are positive acute angles. If sin A=(3/5) and cosB= (12/13) find the value of sin (A+B)

Math
How does the related acute angle help to determine the trigonometric ratios of angles greater than 90 degrees? (in terms of the Cartesian plane) And why is the sin, cos, and tan of the principal angle equal to the sin, cos, and tan of the related acute

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:

math
Can someone please solve them,I just want to see examples,i will do the next 10 myself!!THX! 1)given that tan θ = 2/3 and that θ is acute,find the exact value of: a)sin θ b)cos θ c)sin^2 θ 2)given that sin given that tan θ = (√2)/5 and that θ is

math
In triangle ABC if

math
In triangle ABC if

math
In triangle ABC ,if

Algebra 1
In triangle ABC ,if

geometry
In triangle ABC, if

trig help much appreciated! :))
1. Find the complete exact solution of sin x = . 2. Solve cos 2x – 3sin x cos 2x = 0 for the principal value(s) to two decimal places. 3. Solve tan2 x + tan x – 1 = 0 for the principal value(s) to two decimal places. 4. Prove that tan2 – 1 + cos2

math (trig)
Find sin(x/2) if sin(x)= 0.4 and 3pi/2 < or equal to (x) < or equal to 2pi Let's use cos 2A = 1  2sin2 A and we can match cos x = 1  2sin2 (x/2) so we will need cos x we know sin x = .4 and x is in the fourth quadrant, so the cosine will be positive.

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 

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

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
if a and b are acute angles, sin(a+b)= 56/65, and sin b = 5/13, find sin a

Math
A ray separates a right angles into two acute angles.One of the acute angles measures 37°.what is the measure of the other acute angle?

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

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 +

Mathematics
Given that cosA=4/5 and sinB=15/17 where A and B are acute angles,find the value of cos(AB)

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

MATH
1.)Find the exact solution algebriacally, if possible: (PLEASE SHOW ALL STEPS) sin 2x  sin x = 0 2.) GIVEN: sin u = 3/5, 0 < u < ï/2 Find the exact values of: sin 2u, cos 2u and tan 2u using the doubleangle formulas. 3.)Use the halfangle formulas to

Calculus Vectors
I've come across this math problem and need help on working it out. Ropes 3 m and 5 m in length are fastened to a holiday decoration that is suspended over a town square. The decoration has a mass of 5 kg. The ropes, fastened at different heights, make

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

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 +

Trigonometry
If cos(a)=1/2 and sin(b)=2/3, find sin(a+b), if 1) Both angles are acute; Answer: (sqrt(15)+2)/6 ii) a is an acute angle and pi/2 < b < pi; Answer: (2sqrt(15))/6 2. Find the exact value of the six trigonometric functions of 13pi/12. Partial answer:

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

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

calc
find the area between the xaxis and the graph of the given function over the given interval: y = sqrt(9x^2) over [3,3] you need to do integration from 3 to 3. First you find the antiderivative when you find the antiderivative you plug in 3 to the

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 +

trig
if x and y are positive acute angles, tan x=1/3and tan y =1/4, find the value of sin(xy)

maths 2
The original question I had was write arcsin4 in the form a+ib. I manage and understand how to get so far BUT How do I get from cosacoshbisinasinhb=4 to 2m(pi)+/ iarccosh4 arcsin4 = a + b i > 4 = sin(a + bi) sin(a + bi) = sin(a)cos(bi) + cos(a)

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

PreCal (Trig) Help?
The following relationship is known to be true for two angles A and B: cos(A)cos(B)sin(A)sin(B)=0.957269 Express A in terms of the angle B. Work in degrees and report numeric values accurate to 2 decimal places. So I'm pretty lost on how to even begin

Calculus  Challenge question
Our teacher gave us this problem as a challenge. Some of us have been working on it for a few days help! Prove that the largest area of any quadrilateral is obtained when opposite angles are supplementary. Wow, what a classic and nice question, haven't

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
If A and B are acute angle such that SinA=8/17 and CosB=3/5.Find 1, Cos(A+B) 2, Sin(A+B) 3, Sin(AB)

Mathematics
Trigonometry : Practical application. If x is an acute angle, and tan x = 3\4, evaluate. cos x  sin x \cos x + sin x

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

math
Develop a unit of learning at the end of which learners should be able to: reduce any angle in the first quadrant of a Cartesian plane to a difference of 90 and an acute angle. I have tried it as follows: 1. write down any three acute angles. 2. draw the

math
if a and b are acute angles, sin(a+b)= 56/65, and sin b = 5/13, find sin a

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

Vector
Let 𝑎⃗ and 𝑏 be two vectors in the xy plane making angles 𝜃 and ∅ with the x axis, respectively. Use vector algebra to show that: cos(𝜃 − ∅) = cos 𝜃 cos ∅ + sin 𝜃 sin ∅

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

Trigonometry
I have some trigonometric equations to do, but I'm pretty lost, and I have to get them done in a timely fashion, so any help would be much appreciated. "Solve the following trig equations. Give all the positive values of the angle between 0 degrees and 360

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

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
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

Math sin/cos
On a piece of paper draw and label a right triangle using the given sides, solve for the unknown side and write the trigonometric functions for angles A and B, if a=5 and c=7. I already found side b which equals 2 sqrts of 6. Now I need to find the sin A

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

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

Sin/Cos
I'm having trouble with a concept. I don't understand how the answer was found. 1. Find three other angles, such that cos[beta] = cos [25]. Answers are 25, 335, 335. In my Calc class, the teacher showed it by using a circle, with an angle. Can anyone

Math
If sin x=cos x and x is acute find the value of x

Maths
So there is this question I've been trying to work out, but couldn't come up with a positive answer. Any help on this is highly appreciated. Question : If n,a,b are constants and p is a vector : p=a cos nt + b sin nt. Prove that p*dp/dt=na*b So I worked

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

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 sin/cos
On a piece of paper draw and label a right triangle using the given sides, solve for the unknown side and write the trigonometric functions for angles A and B, if a=5 and c=7. I already found side b which equals 2 sqrts of 6. Now I need to find the sin/cos

MathematicsIntegration
Question: For any positive integer n,show that integrate.[(sin x)^2n dx ] from o  π/2 = [(2n)!*π]/[(2)^(2n+1)*(n!)^2 ] What I thought: Let I =int.[(sinx)^2n dx] And again I= int.[ (sin(π/2x))^2n dx] = int.[ (cos)^2n dx] 2I= int.[(sin x)^2n + (cos

Maths
If cos A=3/5 and A is acute,find sin A,tan A,and sec A.

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(

Maths/Right Triangle
There must be a relationship (formula) between the lengths of the sides of a Right Triangle and the angles opposite these sides. Help Please. Mike. Look at the law os sines or cosines. Law of sines a/sin(A) = b/sin(B) = c/sin(C) Law of cosines a2 = b2 + c2

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.

Calculus
∫((cos^3(x)/(1sin^(2)) What is the derivative of that integral? I have been trying to use trig identities but can't find one to simplify this equation. I can't find one for (cos^3(x) or (1sin^(2)) My options sin(x) + C sin(x) + C (1/4)cos^(4)(x) + C

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)

maths
If tan 0=2 2/5 where 0 is acute, find the values of a)2 sin 0 b)cos (9O0) i could not understand this question.

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(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[xpi/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

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

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)=

functions
A and B are accute angles with sin A =0.7 and cos B= 0.4. Find sin(AB)

Math
If sinx= 5/13, and x is a positive acute angle, find sin (x + 3pi/2)