$$\text { Find all values of } \theta \text {, if } \theta \text { is in the interval } \left[ 0,360 ^ { \circ } \right) \text { and has the given function value. }$$
-$\sec \theta = - \sqrt { 2 }$
A) $45 ^ { \circ }$ and $225 ^ { \circ }$
B) $45 ^ { \circ }$ and $315 ^ { \circ }$
C) $225 ^ { \circ }$ and $315 ^ { \circ }$
D) $135 ^ { \circ }$ and $225 ^ { \circ }$

Question

Quizplus · Accepted Answer

The secant function is the reciprocal of the cosine function. $\sec \theta = - \sqrt { 2 }$ implies $\cos \theta = - \frac{1}{\sqrt{2}} = - \frac{\sqrt{2}}{2}$. The cosine function is negative in the second and third quadrants, where $\theta = 135 ^ { \circ }$ and $225 ^ { \circ }$, respectively.

- sec⁡θ=−2\sec \theta = - \sqrt { 2 }secθ=−2​ A) 45∘45 ^ { \circ }45∘

- $\sec \theta = - \sqrt { 2 }$ A) $45 ^ { \circ }$