Question

The angle 01 is located in Quadrant IV and cos (01) = 3/5

Answer 1

Answer:

4/5

Step-by-step explanation:

Using the Pythagorean Identity,

$\sin {}^{2} ( \alpha ) + \cos {}^{2} ( \alpha ) = 1$

Note that

$\cos {}^{2} ( \alpha )$

is basically

$( \cos( \alpha ) ) {}^{2}$

So that means

$\cos {}^{2} ( \alpha ) = ( \frac{3}{5} ) {}^{2} = \frac{9}{25}$

So we have

$\sin {}^{2} ( \alpha ) + \frac{9}{25} = 1$

Solve for sin a.

$\sin {}^{2} ( \alpha ) = \frac{25}{25} - \frac{9}{25}$

25/25 is the same as 1.

$\sin {}^{2} ( \alpha ) = \frac{16}{25}$

Take the square root.

since sin is positive in the first quadrant, take the principal square root.

$\sin( \alpha ) = \frac{ \sqrt{16} }{ \sqrt{25} }$

$\sin( \alpha ) = \frac{4}{5}$