Question

Given that sin ø 21/29, what is the value of cos ø, for 0° < ø < 90%

Answer 1

`(20)/(29)`

Explanation:

Let x replace theta.

Apply pythagorean trig identity

`\sin {}^(2) (x) + \cos {}^(2) (x) = 1`

`((21)/(29) ) {}^(2) + \cos {}^(2) (x) = 1`

`(441)/(841) + \cos {}^(2) (x) = 1`

`\cos {}^(2) (x) = 1 - (441)/(841)`

`\cos {}^(2) (x) = (400)/(841)`

`\cos(x) = (20)/(29)`

Cosine is positve in 1st quadrant so the answer is

`(20)/(29)`