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

Question

Find any zeros of $r$ on the interval $0 \leq \theta < 2 \pi$.
$$r = \sqrt { 3 } + 2 \cos \theta$$
A) zeros: $\frac { \pi } { 6 } , \frac { 11 \pi } { 6 }$
B) zeros: $\frac { 5 \pi } { 6 } , \frac { 7 \pi } { 6 }$
C) zeros: $\frac { 5 \pi } { 3 } , \frac { 7 \pi } { 3 }$
D) zeros: $\frac { \pi } { 3 } , \frac { 11 \pi } { 3 }$
E) zeros: $\frac { 5 \pi } { 2 } , \frac { 7 \pi } { 2 }$

Quizplus · Accepted Answer

To find the zeros of $r$, set the equation equal to zero and solve for $\theta$:$$0 = \sqrt{3} + 2\cos\theta$$$$\Rightarrow -\sqrt{3} = 2\cos\theta$$$$\Rightarrow \cos\theta = -\frac{\sqrt{3}}{2}$$The values of $\theta$ that satisfy this equation in the interval $0 \leq \theta < 2\pi$ are $\frac{5\pi}{6}$ and $\frac{7\pi}{6}$, which correspond to the angles where the cosine function equals $-\frac{\sqrt{3}}{2}$.

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 $0 \leq \theta < 2 \pi$