Assume that $ \theta $ is an acute angle in a right triangle satisfying the given conditions. Evaluate the indicated trigonometric
function.
-$\csc \theta = \frac { 5 } { 2 } ; \cos \theta$
A) $\frac { \sqrt { 21 } } { 5 }$
B) $\frac { 2 } { 5 }$
C) $\frac { 2 } { \sqrt { 21 } }$
D) $\frac { \sqrt { 21 } } { 2 }$

Question

Quizplus · Accepted Answer

Given $\csc \theta = \frac{5}{2}$, we know $\sin \theta = \frac{1}{\csc \theta} = \frac{2}{5}$. Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we find $\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - \left(\frac{2}{5}\right)^2} = \sqrt{\frac{21}{25}} = \frac{\sqrt{21}}{5}$.

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