Question 876536
Given that cos theta = -5/13 with theta in quadrant II, find tan 2 theta
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You are working with a (5-12-13) reference right triangle in quadrant II
{{{cos(theta)=-5/13}}}
{{{sin(theta)=12/13}}}
{{{sin(2theta)=2sin(theta)cos(theta)=2*12/13*-5/13=-120/169}}}
{{{cos(2theta)=cos^2(theta)-sin^2(theta)=25/169-144/69=-119/69}}}
{{{tan(2theta)=sin(2theta)/cos(2theta)=120/119}}}
Calculator check:
cos(theta)=-5/13
theta≈112.62
2theta≈225.24}}}
tan(2theta)≈tan(225.24)≈1.0084…
exact value as calculated=120/119≈1.0084…
let me know if my answer is correct and the procedure is understandable.