Find all solutions of the following equation on the interval $[ 0,2 \pi )$.
$$\cot ( x ) + \sqrt { 3 } = 0$$
A) $\frac { 5 \pi } { 6 } , \frac { \pi } { 6 } , \frac { 11 \pi } { 6 } , \frac { 7 \pi } { 6 }$
B) $\frac { \pi } { 3 } , \frac { 4 \pi } { 3 }$
C) $\frac { 5 \pi } { 6 } , \frac { 11 \pi } { 6 }$
D) $\frac { 2 \pi } { 3 } , \frac { 5 \pi } { 3 }$
E) $\frac { \pi } { 6 } , \frac { 7 \pi } { 6 }$

Question

Quizplus · Accepted Answer

The equation $\cot(x) + \sqrt{3} = 0$ can be rewritten as $\cot(x) = -\sqrt{3}$. This means that the tangent of the angle is $\sqrt{3}$, which occurs at angles $\frac{5\pi}{6}$ and $\frac{11\pi}{6}$ within the given interval $[0, 2\pi)$.

Find All Solutions of the Following Equation on the Interval [0,2π)[ 0,2 \pi )[0,2π)

Find All Solutions of the Following Equation on the Interval $[ 0,2 \pi )$