An equation of the terminal side of an angle in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of . Do not use a calculator.
-$2 x + 7 y = 0 , x \geq 0 ; \quad$ Find $\cot \theta$
A) $- \frac { 7 } { 2 }$
B) $- \frac { 2 } { 7 }$
C) $\frac { 7 } { 2 }$
D) $\frac { \sqrt { 53 } } { 2 }$

Question

Quizplus · Accepted Answer

The equation $2x + 7y = 0$ can be rewritten as $y = -\frac{2}{7}x$, which represents a line through the origin with a slope of $-\frac{2}{7}$. The slope of the line is equal to the tangent of the angle $\theta$ that the line makes with the positive x-axis, so $\tan \theta = -\frac{2}{7}$. The cotangent is the reciprocal of the tangent, so $\cot \theta = -\frac{7}{2}$.

An Equation of the Terminal Side of an Angle in Standard