Which is sin 2 theta when cos theta=-frac{3}{5} and 0

Question

Which is sin 2 theta when cos theta=-frac{3}{5} and 0<theta<pi ?

Accepted Answer

Step:1 ：Given: (costheta = -frac{3}{5}) and (0 < theta < pi)Step:2 ：Use the Pythagorean identity: (sin^2theta + cos^2theta = 1)Step:3 ：Calculate (sin^2theta = 1 - cos^2theta = 1 - left(-frac{3}{5}right)^2 = frac{16}{25})Step:4 ：Find (sintheta = sqrt{frac{16}{25}} = frac{4}{5}) since (sintheta) is positiveStep:5 ：Use the double angle formula: (sin 2theta = 2sinthetacostheta)Step:6 ：Calculate (sin 2theta = 2left(frac{4}{5}right)left(-frac{3}{5}right) = -frac{24}{25})Step:7 ：(boxed{-frac{24}{25}}) is the final answer

Answer

Step: 1 ：Given: (costheta = -frac{3}{5}) and (0 < theta < pi)Step: 2 ：Use the Pythagorean identity: (sin^2theta + cos^2theta = 1)Step: 3 ：Calculate (sin^2theta = 1 - cos^2theta = 1 - left(-frac{3}{5}right)^2 = frac{16}{25})Step: 4 ：Find (sintheta = sqrt{frac{16}{25}} = frac{4}{5}) since (sintheta) is positiveStep: 5 ：Use the double angle formula: (sin 2theta = 2sinthetacostheta)Step: 6 ：Calculate (sin 2theta = 2left(frac{4}{5}right)left(-frac{3}{5}right) = -frac{24}{25})Step: 7 ：(boxed{-frac{24}{25}}) is the final answer

Which is $\sin 2 \theta$ when $\cos \theta=-\frac{3}{5}$ and $0< \theta< \pi$ ?

Answer

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