SOLUTION: Find sin 2x, cos 2x, and tan 2x from the given information. tan x = − 12/5, x in Quadrant II

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Question 922456: Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = − 12/5, 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 = − 12/5, x in Quadrant II
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Given data shows you are working with a (5-12-13) reference right triangle in quadrant II
..
sinx=12/13
cosx=-5/13
..
sin2x=2sinxcosx=2*12/13*-5/13=-120/169
cos2x=cos^x-sin^2x=25/69-144/69=-119/169
tan2x=sin/cos=120/119
..
Check:
tanx=-12/5
x=112.62˚
2x=225.24˚
..
sin2x=sin(225.24)≈-0.7100
Exact value=-120/169≈-0.7100
..
costx=cos(225.24)≈-0.7041
Exact value=-119/169≈-0.7041
..
tan2x=tan(225.24)≈1.0084
Exact value=-120/119≈-1.0084