Find any zeros of $r$ on the interval $0 \leq \theta

Question

Find any zeros of $r$ on the interval $0 \leq \theta < 2 \pi$.
$$r = \sqrt { 2 } - 2 \cos \theta$$
A) zeros: $\frac { 3 \pi } { 4 } , \frac { 5 \pi } { 4 }$
B) zeros: $\frac { \pi } { 4 } , \frac { 7 \pi } { 4 }$
C) zeros: $\frac { \pi } { 2 } , \frac { 7 \pi } { 2 }$
D) zeros: $\frac { 3 \pi } { 2 } , \frac { 5 \pi } { 2 }$
E) zeros: $\frac { \pi } { 8 } , \frac { 7 \pi } { 8 }$

Quizplus · Accepted Answer

To find the zeros of $r$, we set the equation equal to zero and solve for $\theta$:$$0 = \sqrt{2} - 2\cos\theta$$$$2\cos\theta = \sqrt{2}$$$$\cos\theta = \frac{\sqrt{2}}{2}$$The solutions to $\cos\theta = \frac{\sqrt{2}}{2}$ on the interval $0 \leq \theta < 2\pi$ are $\theta = \frac{\pi}{4}$ and $\theta = \frac{7\pi}{4}$, which correspond to the angles where the cosine function equals $\frac{\sqrt{2}}{2}$.

Find Any Zeros Of rrr On the Interval 0≤θ<2π0 \leq \theta < 2 \pi0≤θ<2π

Find Any Zeros Of $r$ On the Interval $0 \leq \theta < 2 \pi$