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

Question

asked Mar 21, 2022 49.2k views

1 Answer

Ddiez · Answer 1 · 2022-03-25T20:15:54+0000

Answer:

(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)