# Trigonometry

4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/17. Angles x and y are in the fourth quadrant.

5. Find the exact value for cos 165degrees using the half-angle identity.

1. Solve: 2 cos^2x - 3 cosx + 1 = 0 for 0 less than or equal to x <2pi.

2. Solve: 2 sinx - 1 = 0 for 0degrees less than or equal to x <360degrees.

3. Solve: sin^2x = cos^2x for 0degrees is less than or equal to x < 360degrees.

4. Solve sinx - 2sinx cosx = 0 for 0 is less than or equal to x < 2pi.

1. 👍 1
2. 👎 0
3. 👁 1,265
1. #4
sin(x+y) = sinx cosy + cosx siny

so we need the cosx and the siny
from sinx = -4/5 we know we are dealing with the 3,4,5 right-angled triangle, so in the fourth quadrant cosx = 3/5
from cosy = 15/17 we know we are dealing with the 8,15,17 right-angled triangle
so in the fourth quadrant, siny = -8/17
then
sin(x+y) = sinx cosy + cosx siny
= (-4/5)(15/17) + (3/5)(-8/17)
= -84/85

1. 👍 0
2. 👎 0
2. cos 2A = 2cos^2 A - 1
let A = 165, then 2A = 330
so let's find cos 330
cos(330)
= cos(360-30)
= cos360 cos30 + sin360 sin30
= (1)(√3/2) + (0)(1/2) = √3/2

then √3/2 = 2cos^2 165 - 1
(√3 + 2)/4 = cos^2 165
cos 165 = -√(√3 + 2))/2

(algebraically, our answer would have been ± , but I picked the negative answer since 165 is in the second quadrant, and the cosine is negative in the second quadrant)

1. 👍 0
2. 👎 0
3. I will give you hints for the rest,
you do them, and let me know what you get.

#1 factor it as
(2cosx - 1)(cosx -1) = 0
so cosx - 1/2 or cosx = 1
take it from there, you should get 3 answers.

#2, the easiest one
take the 1 to the other side, then divide by 2,

#3, take √ of both sides to get
sin 2x = ± cos 2x
sin2x/cos2x = ± 1
tan 2x = ± 1 etc

#4 factor out a sinx etc

1. 👍 0
2. 👎 0

## Similar Questions

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

2. ### Trig.......

I need to prove that the following is true. Thanks (2tanx /1-tan^x)+(1/2cos^2x-1)= (cosx+sinx)/(cosx - sinx) and thanks ........... check your typing. I tried 30º, the two sides are not equal, they differ by 1 oh , thank you Mr

3. ### Pre-Calc

I am really struggling with how to do these problems, I posted them a few minutes ago but the answers/work shown was incorrect. 1) a) Use an Addition or Subtraction Formula to write the expression as a trigonometric function of

4. ### Math help again

cos(3π/4+x) + sin (3π/4 -x) = 0 = cos(3π/4)cosx + sin(3π/4)sinx + sin(3π/4)cosx - cos(3π/4)sinx = -1/sqrt2cosx + 1/sqrt2sinx + 1/sqrt2cosx - (-1/sqrt2sinx) I canceled out -1/sqrt2cosx and 1/sqrt2cosx Now I have 1/sqrt sinx +

1. ### 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)

Which of the following are trigonometric identities? (Can be more then one answer) tanx cosx cscx = 1 secx-cosx/secs=sin^2x 1-tanxtany=cos(x+y)/cosxcosy 4cosx sinx = 2cosx + 1 - 2sinx Find all solutions to the equation cosx

3. ### math;)

The equation 2sinx+sqrt(3)cotx=sinx is partially solved below. 2sinx+sqrt(3)cotx=sinx sinx(2sinx+sqrt(3)cotx)=sinx(sinx) 2sin^2x+sqrt(3)cosx=sin^2x sin^2x+sqrt(3)cosx=0 Which of the following steps could be included in the

4. ### 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)

1. ### math- Trigonometry

If cos degree equals to 0.8641 What is Sin degree? I have no idea how to find this. Please help me. I got help from two people, but I'm not getting the answer and how they got the numbers either. Someone says: cos^2+sin^2=1

2. ### 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

3. ### Math

1) evaluate without a calculator: a)sin(3.14/4) b) cos(-3(3.14)/4) c) tan(4(3.14)/3) d) arccos(- square root of three/2) e) csctheata=2 2) verify the following identities: a) cotxcosx+sinx=cscx b)[(1+sinx)/ cosx] + [cosx/

4. ### 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