Give the exact value of the expression.
-$\cos \left( \arcsin \frac { 1 } { 4 } \right)$
A) $\frac { \sqrt { 15 } } { 4 }$
B) $\frac { 4 \sqrt { 15 } } { 15 }$
C) $\frac { \sqrt { 15 } } { 2 }$
D) $\frac { 2 \sqrt { 15 } } { 15 }$

Question

Quizplus · Accepted Answer

To find the exact value of $\cos(\arcsin(\frac{1}{4}))$, we can use the Pythagorean identity $\sin^2(x) + \cos^2(x) = 1$. If $\sin(x) = \frac{1}{4}$, then $\cos(x) = \sqrt{1 - \sin^2(x)} = \sqrt{1 - \left(\frac{1}{4}\right)^2} = \sqrt{1 - \frac{1}{16}} = \sqrt{\frac{15}{16}} = \frac{\sqrt{15}}{4}$.

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

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