Give the exact value of the expression.
-$\cos \left( 2 \arcsin \frac { 1 } { 4 } \right)$

Name: Give the exact value of the expression. -$\cos \left( 2 \arcsin \frac { 1 } { 4 } \right)$
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Question

Quizplus · Accepted Answer

Using the identity $\cos(2\theta) = 1 - 2\sin^2(\theta)$, let $\theta = \arcsin\left(\frac{1}{4}\right)$. Thus, $\sin(\theta) = \frac{1}{4}$, and substituting into the identity gives $\cos(2\theta) = 1 - 2\left(\frac{1}{4}\right)^2 = 1 - 2\left(\frac{1}{16}\right) = 1 - \frac{1}{8} = \frac{7}{8}$.

Give the Exact Value of the Expression cos⁡(2arcsin⁡14)\cos \left( 2 \arcsin \frac { 1 } { 4 } \right)cos(2arcsin41​)

Give the Exact Value of the Expression $\cos \left( 2 \arcsin \frac { 1 } { 4 } \right)$