Find Exact Value of cosθ Given sinθ=19/51

[cosmictide]

Hi guys,

This has caused me some confusion. Any help in this regard would be greatly appreciated.

Homework Statement

Given that $\theta$ is an acute angle with sin$\theta$=19/51 find the exact value of cos$\theta$

Homework Equations

The Attempt at a Solution

All I seem to be getting based on my calculations are approximations. I have no idea how to actually obtain the exact value. Initially I took the inverse of sin$\theta$ to get $\theta$=21.872...degree. Therefore the cos$\theta$=0.928...I also tried using a right-angled triangle and finding the adjacent which I calculated to be 47.328... and dividing adj by hyp to see whether I get an exact value but got the same answer as before.

Any help in this regard would be greatly appreciated.

Thanks in advance.

 

[BvU]

What about $\sin^2 + \cos^2 = 1$, exactly ? It means you get a square root in your answer, but it definitely is exact.

 

[cosmictide]

What about $\sin^2 + \cos^2 = 1$, exactly ? It means you get a square root in your answer, but it definitely is exact.

Genius.

Thank you so much, I can't believe I didn't think of that.