Find the exact value of the expression.884:890
-$\sin \left[ 2 \cos ^ { - 1 } \left( - \frac { 3 } { 5 } \right) \right]$
A) $- \frac { 12 } { 25 }$

B) $- \frac { 24 } { 25 }$

C) $\frac { 12 } { 25 }$

D) $\frac { 24 } { 25 }$

Question

Find the exact value of the expression.884:890
-$\sin \left[ 2 \cos ^ { - 1 } \left( - \frac { 3 } { 5 } \right) \right]$
A) $- \frac { 12 } { 25 }$

B) $- \frac { 24 } { 25 }$

C) $\frac { 12 } { 25 }$

D) $\frac { 24 } { 25 }$

Quizplus · Accepted Answer

The expression involves finding $\sin(2\theta)$ where $\theta = \cos^{-1}(-\frac{3}{5})$. Using the identity $\sin(2\theta) = 2\sin(\theta)\cos(\theta)$, we first find $\sin(\theta)$ using $\sin^2(\theta) + \cos^2(\theta) = 1$. Since $\cos(\theta) = -\frac{3}{5}$, $\sin(\theta) = \frac{4}{5}$. Thus, $\sin(2\theta) = 2 \times \frac{4}{5} \times -\frac{3}{5} = -\frac{24}{25}$.

Find the Exact Value of the Expression sin⁡[2cos⁡−1(−35)]\sin \left[ 2 \cos ^ { - 1 } \left( - \frac { 3 } { 5 } \right) \right]sin[2cos−1(−53​)]

Find the Exact Value of the Expression $\sin \left[ 2 \cos ^ { - 1 } \left( - \frac { 3 } { 5 } \right) \right]$