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

Question

psymon · Answer

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:

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Now using that, find the cosine :3

anonymous · Answer

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

psymon · Answer

No, we find x through pythagorean theorem.

anonymous · Answer

ok 

$$1^{2} + x ^{2} = 4^{2}$$
$$x^{2} = 16-1$$
$$x ^{2}=15$$
$$x=\sqrt{15}$$

psymon · Answer

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

anonymous · Answer

cos= $$\frac{ \sqrt{15} }{ 4}$$

psymon · Answer

That's your answer :3

anonymous · Answer

Thank you very much :)

psymon · Answer

Yep, np :3