Choose the one alternative that best completes the statement or answers the question.
-$7 \cot ^ { 2 } x - 5 = 0$
A) $103.2 ^ { \circ } , 145.2 ^ { \circ } , 283.2 ^ { \circ } , 325.2 ^ { \circ }$
B) $51.8 ^ { \circ } , 128.2 ^ { \circ }$
C) $70.5 ^ { \circ } , 109.5 ^ { \circ } , 180.0 ^ { \circ }$
D) $49.8 ^ { \circ } , 130.2 ^ { \circ } , 229.8 ^ { \circ } , 310.2 ^ { \circ }$

Question

Quizplus · Accepted Answer

First, solve the equation for $\cot^2 x$: $7\cot^2 x - 5 = 0$ implies $\cot^2 x = \frac{5}{7}$. Taking the square root gives $\cot x = \pm\sqrt{\frac{5}{7}}$. The cotangent function is positive in the first and third quadrants, and negative in the second and fourth quadrants. The angles provided in option D correspond to these quadrants and the correct values of $\cot x$.

Choose the One Alternative That Best Completes the Statement or Answers