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3 years ago

13

Find sin 2x, cos 2x, and tan 2x from the given information.

1 answer:

krok68 [10]3 years ago

3 0

<span>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</span>

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