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In the problem, sin θ and cos θ are given. Find the exact value of the indicated trigonometric function.
-$\sin \theta = \frac { 1 } { 4 } , \cos \theta = \frac { \sqrt { 15 } } { 4 } \quad$ Find $\sec \theta$
A) $\sqrt { 15 }$
B) 4
C) $\frac { \sqrt { 15 } } { 15 }$
D) $\frac { 4 \sqrt { 15 } } { 15 }$

Question

Quizplus · Accepted Answer

The secant function is the reciprocal of the cosine function. Therefore, $\sec \theta = \frac{1}{\cos \theta} = \frac{1}{\frac{\sqrt{15}}{4}} = \frac{4}{\sqrt{15}}$. Rationalizing the denominator gives $\frac{4 \sqrt{15}}{15}$.

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