Posted by **Luis** on Sunday, May 13, 2012 at 5:04pm.

Currently in school we're learning about proving identities and for extra credit I got this problem.

cosB= -8/17 in quad II and I have to find sin 7B.

I have gotten this far:

sin7B= sin(3B+4B)

sin3Bcos4B+sin4Bcos3B

my problem I can't figure out how to further break it down. After that I can do the rest.

- pre-calculus -
**Steve**, Sunday, May 13, 2012 at 5:31pm
This is just a make-work problem, providing no added insight. Just plug and chug.

You have a 8-15-17 triangle in QII or QIII. Let's go with QII for now.

sinB = 15/17

sin2B = 2sinVcosB = 2(-8/17)(15/17) = -240/17^2

cos2B = cos^2B - sin^2B = 64/289 - 225/289 = -161/17^2

sin4B = 2sin2Bcos2B = 2(-240/289)(-161/289) = 77280/17^4

cos4B = cos^2 2B - sin^2 2B = 64^2/17^4 - 240^2/17^4 = -53504/17^4

sin3B = sinBcos2B + cosBsin2B

sin7B = sin3Bcos4B + cos3Bsin4B

I'll let you do the arithmetic. *whew*

## Answer This Question

## Related Questions

- math - find all solutions in the interval [0,2 pi) sin(x+(3.14/3) + sin(x- 3.14/...
- pre-calculus - I am having trouble with trigenometric identities I cannot figure...
- chemistry - I have been knocking around this question for what seems to be an ...
- trig - find the exact value given that cosA=(1/3) in quad I, sin B=(-1/2) in ...
- Algebra 1 - How would you solve the problem (w - 2)^2 ???? So far I've gotten w^...
- Pre-calculus - If cosx=4/5, cosy=12/13 in Quad. IV, find sin(x+y)
- Pre-calculus - If cosx=4/5, cosy=12/13 in Quad. IV, find sin(x+y)
- trig - find the exact value given that cosA=(1/3) in quad I, sin B=(-1/2) in ...
- trig - find the exact value given that cosA=(1/3) in quad I, sin B=(-1/2) in ...
- Public High School Pre Calculus HH - Ok I do not know how to do this problem. I ...

More Related Questions