Question

cos(arcsin(7/8))
=

Answer 1

To find \(\cos(\arcsin(7/8))\), we can use the relationship between sine and cosine in a right triangle.

Let \(\theta = \arcsin(7/8)\). This means that \(\sin(\theta) = 7/8\).

Now, we can visualize \(\theta\) in a right triangle where:
- The opposite side to the angle \(\theta\) is 7.
- The hypotenuse is 8.

To find the adjacent side \(x\), we can use the Pythagorean theorem:

\[
x^2 + 7^2 = 8^2
\]

\[
x^2 + 49 = 64
\]

\[
x^2 = 64 - 49
\]

\[
x^2 = 15
\]

\[
x = \sqrt{15}
\]

Now we can find \(\cos(\theta)\):

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{\sqrt{15}}{8}
\]

Therefore,

\[
\cos(\arcsin(7/8)) = \frac{\sqrt{15}}{8}
\]