Mathematics
tymeisha
22

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

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hanan1

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

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