Find the absolute extreme values of the function on the interval.
-$$f ( \theta ) = \sin \left( \theta + \frac { \pi } { 2 } \right) , 0 \leq \theta \leq \frac { 5 \pi } { 4 }$$
A) absolute maximum is 1 at $\theta = 0$; absolute minimum is $- 1$ at $\theta = \pi$
B) absolute maximum is 1 at $\theta = \frac { 1 } { 2 } \pi$; absolute minimum is $- 1$ at $\theta = \frac { 1 } { 2 } \pi$,
C) absolute maximum is 1 at $\theta = \frac { 3 } { 2 } \pi$; absolute minimum is $- 1$ at $\theta = \frac { 1 } { 2 } \pi$,
D) absolute maximum is 1 at $\theta = \frac { 1 } { 2 } \pi$; absolute minimum is $- 1$ at $\theta = \frac { 1 } { 2 } \pi$

Question

Quizplus · Accepted Answer

We have $f(	heta) = \cos(	heta)$, so the maximum absolute value is $1$ and is achieved at $	heta = 0$. The minimum absolute value is also $1$ and is achieved at $	heta = \pi$.

Find the Absolute Extreme Values of the Function on the Interval