Solve the equation for solutions in the interval [0°, 360°). Round to the nearest degree.
-$$\cot \frac { \theta } { 3 } = 1$$
A) $\left\{ 0 ^ { \circ } , 90 ^ { \circ } , 180 ^ { \circ } , 270 ^ { \circ } \right\}$
B) $\left\{ 135 ^ { \circ } \right\}$
C) $\left\{ 33 ^ { \circ } , 57 ^ { \circ } , 123 ^ { \circ } , 147 ^ { \circ } , 213 ^ { \circ } , 237 ^ { \circ } , 303 ^ { \circ } \right\}$
D) $\left\{ 0 ^ { \circ } , 45 ^ { \circ } , 90 ^ { \circ } , 180 ^ { \circ } , 225 ^ { \circ } , 270 ^ { \circ } , 315 ^ { \circ } \right\}$

Question

Quizplus · Accepted Answer

The cotangent function is positive in quadrants I and III. In the interval [0°, 360°), the only angle in quadrant I that satisfies the equation is 33°. The only angle in quadrant III that satisfies the equation is 147°.

Solve the Equation for Solutions in the Interval [0°, 360°) cot⁡θ3=1\cot \frac { \theta } { 3 } = 1cot3θ​=1

Solve the Equation for Solutions in the Interval [0°, 360°) $\cot \frac { \theta } { 3 } = 1$