Determine all solutions of the equation in radians.
-$\cos \theta = \frac { 20 } { 29 } , \quad \sin \theta

Question

Determine all solutions of the equation in radians.
-$\cos \theta = \frac { 20 } { 29 } , \quad \sin \theta < 0 \quad$ Find $\sin ( 2 \theta )$
A) $- \frac { 41 } { 841 }$
B) $\frac { 840 } { 841 }$
C) --------
D) $- \frac { 840 } { 841 }$

Quizplus · Accepted Answer

Given $\cos \theta = \frac{20}{29}$ and $\sin \theta < 0$, we can find $\sin \theta$ using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$. Solving for $\sin \theta$, we get $\sin \theta = -\sqrt{1 - \cos^2 \theta} = -\sqrt{1 - \left(\frac{20}{29}\right)^2} = -\frac{21}{29}$, since $\sin \theta < 0$. Then, $\sin(2\theta) = 2\sin \theta \cos \theta = 2 \left(-\frac{21}{29}\right) \left(\frac{20}{29}\right) = -\frac{840}{841}$.

Determine All Solutions of the Equation in Radians cos⁡θ=2029,sin⁡θ<0\cos \theta = \frac { 20 } { 29 } , \quad \sin \theta < 0 \quadcosθ=2920​,sinθ<0

Determine All Solutions of the Equation in Radians $\cos \theta = \frac { 20 } { 29 } , \quad \sin \theta < 0 \quad$