Find all values of , if is in the interval [0, 360°) 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 $\cos \theta = - \frac{1}{\sqrt{2}}$, which corresponds to angles in the second and third quadrants where cosine is negative. The angles with this cosine value are $135^\circ$ and $225^\circ$.

Find All Values of , If Is in the Interval sec⁡θ=−2\sec \theta = - \sqrt { 2 }secθ=−2​

Find All Values of , If Is in the Interval $\sec \theta = - \sqrt { 2 }$