SOLUTION: Find sin 2x, cos 2x, and tan 2x from the given information. tan x = − 15/8 x in Quadrant II

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Question 955464: Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = −
15/8 x in Quadrant II
Answer by lwsshak3(11628) About Me  (Show Source):
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Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = − 15/8 x in Quadrant II
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Hypotenuse of reference right triangle in quadrant II=√((15^2)+(8^2))=√(225+64)=√289=17
sinx=15/17
cosx=8/17
sin2x=2sinxcosx=2*15/17*8/17=240/289
cos2x=cos^x-sin^2x=(8/17)^2-(15/17)^2=64/289-225/289=-161/289
tan2x=sin2x/cos2x=-240/161
Check:
tanx=-15/8
x≈118.0724˚
2x≈236.145
tan2x=tan236.145≈-1.4907
exact value as computed=-240/161≈-1.4907