Question

Find the exact value of cos(arcsin(1/4)). For full credit, explain your reasoning.

Answer 1

Let \(u=\sin^{-1}\left(\dfrac{1}{4}\right)\), so you have \(\sin u=\dfrac{1}{4}\).

How would you go about finding \(\cos u\)?

Answer 2

A/h

Answer 3

Right, which means
\[\cos u=\frac{t}{4}\]
What's the value of \(t\) ?

Answer 4

Since you have a right triangle with two of the known sides, how would you solve for the unknown side?

Answer 5

Pythagreom theorem

Answer 6

Right. What do you get for \(t\) ?

Answer 7

sqrt of 15

Answer 8

Right again. So \(\cos u=\cos\left[\sin^{-1}\left(\dfrac{1}{4}\right)\right]=\dfrac{\sqrt{15}}{4}\)