Use a reference triangle in an appropriate quadrant to find the angle.
-$\sec ^ { - 1 } ( \sqrt { 2 } )$
A) $\frac { 3 \pi } { 4 }$
B) $\frac { 7 \pi } { 4 }$
C) $\frac { \pi } { 4 }$
D) $\frac { \pi } { 4 } \pm 2 \pi \mathrm { n } , \frac { 7 \pi } { 4 } \pm 2 \pi \mathrm { n }$

Question

Quizplus · Accepted Answer

The secant function is the reciprocal of the cosine function. $\sec^{-1}(\sqrt{2})$ corresponds to $\cos^{-1}(1/\sqrt{2})$, which is $\pi/4$ in the first quadrant.

Use a Reference Triangle in an Appropriate Quadrant to Find sec⁡−1(2)\sec ^ { - 1 } ( \sqrt { 2 } )sec−1(2​)

Use a Reference Triangle in an Appropriate Quadrant to Find $\sec ^ { - 1 } ( \sqrt { 2 } )$