Question 45148: hello :
i really could use some help with this problem. i am a little confused with this one
thank you in advance, it is greatly appreciated.
terry
find the exact value of : sin 2 theta, cos 2 theta, tan 2 theta
sin theta = - 4\5 270 degrees less than theta. theta less than 360 degrees
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! find the exact value of : sin 2 theta, cos 2 theta, tan 2 theta
sin theta = - 4\5 270 degrees less than theta. theta less than 360 degrees
Since sin(theta)=-4/5 in the 4th quadrant,
cos(theta)=3/5 and tan(theta)=sin/cos = -4/3
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Then sin(2theta) = 2sin(theta)cos(theta)
=2(-4/5)(3/5)=-24/25
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cos(2theta)= cos^2(theta)-sin^2(theta)
=(3/5)^2 - (-4/5)^2
=9/25-16/25
=-7/25
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tan(2theta)=(2tan(theta))/(1-tan^2(theta)
=(2(-4/3))/(1-(-4/3)^2)
=(-8/3)/(-7/9)
=24/7
Cheers,
Stan H.
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