Question

Find the exact value of cos(arcsin(one fourth)). For full credit, explain your reasoning.

Answer 1

So what this question basically asks is find the cosine of a triangle that has a sin value of 1/4. So we want a triangle that has a sin (opposite/hypotenuse) of 1/4 and then find thecosine of that triangle. So doing that we can draw this:




Now using that, find the cosine :3

Answer 2

sin^-1(1/4)=x
right?

Answer 3

No, we find x through pythagorean theorem.

Answer 4

ok

\[1^{2} + x ^{2} = 4^{2}\]
\[x^{2} = 16-1\]
\[x ^{2}=15\]
\[x=\sqrt{15}\]

Answer 5

Correct. So now with all 3 sides, what is the cosine of that triangle?

Answer 6

cos= \[\frac{ \sqrt{15} }{ 4}\]

Answer 7

That's your answer :3

Answer 8

Thank you very much :)

Answer 9

Yep, np :3