pre-calculus

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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 -

    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*

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