Question

the angle 01 is located in quadrant IV, and sin(01)= -10/13 what is the value of cos(01)?

Answer 1

The Pythagorean identity is

$\cos ^2\theta=1-\sin ^2\theta$

we have

$\sin (\theta_1)=-\frac{10}{13}$

we substitute the values in the identity

$\cos ^2(\theta_1)=1-(-\frac{10}{13})^2$$\cos (\theta_1)=\sqrt[]{1-(-\frac{10}{13})^2}=\frac{\sqrt[]{69}}{13}$