Find the exact value of $\sec \left( \frac { 3 \pi } { 4 } \right)$ and $\csc \left( - \frac { 11 \pi } { 4 } \right)$
A) $\frac { - \sqrt { 2 } } { 2 }$
, $- \sqrt { 2 }$

B) $- \sqrt { 2 }$
, $\frac { - 1 } { 2 }$

C) $\frac { - \sqrt { 2 } } { 3 }$
, $- \frac { \sqrt { 2 } } { 3 }$

D) $- \sqrt { 2 }$
, $- \sqrt { 2 }$

E) $- 1$
, $- 1$

Question

Find the exact value of $\sec \left( \frac { 3 \pi } { 4 } \right)$ and $\csc \left( - \frac { 11 \pi } { 4 } \right)$
A) $\frac { - \sqrt { 2 } } { 2 }$
, $- \sqrt { 2 }$

B) $- \sqrt { 2 }$
, $\frac { - 1 } { 2 }$

C) $\frac { - \sqrt { 2 } } { 3 }$
, $- \frac { \sqrt { 2 } } { 3 }$

D) $- \sqrt { 2 }$
, $- \sqrt { 2 }$

E) $- 1$
, $- 1$

Quizplus · Accepted Answer

$\sec \left( \frac { 3 \pi } { 4 } \right) = \frac{1}{\cos \left( \frac { 3 \pi } { 4 } \right)} = \frac{1}{-\frac{\sqrt{2}}{2}} = -\sqrt{2}$. $\csc \left( - \frac { 11 \pi } { 4 } \right) = \frac{1}{\sin \left( - \frac { 11 \pi } { 4 } \right)} = \frac{1}{\sin \left( \frac { \pi } { 4 } \right)} = \frac{1}{\frac{\sqrt{2}}{2}} = \sqrt{2}$, but since the angle is negative, it cycles back to a positive equivalent, maintaining the value.

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