Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$$\sin \theta = \frac { 9 } { 10 } ; \cos \theta$$
A) $\frac { 10 } { 9 }$
B) $\frac { 10 } { \sqrt { 19 } }$
C) $\frac { \sqrt { 19 } } { 10 }$
D) $\frac { \sqrt { 19 } } { 9 }$

Question

Quizplus · Accepted Answer

The Pythagorean theorem states that $\sin^2 \theta + \cos^2 \theta = 1$. Given $\sin \theta = \frac{9}{10}$, we find $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - \left(\frac{9}{10}\right)^2} = \sqrt{1 - \frac{81}{100}} = \sqrt{\frac{19}{100}} = \frac{\sqrt{19}}{10}$.

Assume That θ \theta θ Is an Acute Angle in a Right Triangle Satisfying the a Right

Assume That $\theta$ Is an Acute Angle in a Right Triangle Satisfying the a Right