An equation of the terminal side of an angle $\theta$ in standard position is given along with a restriction on x. Find the
indicated trigonometric function value of $\theta$ . Do not use a calculator.
-$4 x + 3 y = 0 , x \geq 0 ; \quad$ Find $\cot \theta$
A) $- \frac { 3 } { 4 }$
B) $\frac { 5 } { 4 }$
C) $\frac { 3 } { 4 }$
D) $- \frac { 4 } { 3 }$

Question

Quizplus · Accepted Answer

The equation $4x + 3y = 0$ can be rewritten as $y = -\frac{4}{3}x$. This represents a line through the origin with a slope of $-\frac{4}{3}$. The slope of the line is the tangent of the angle $\theta$ that the line makes with the positive x-axis, so $\tan(\theta) = -\frac{4}{3}$. The cotangent is the reciprocal of the tangent, so $\cot(\theta) = -\frac{3}{4}$.

An Equation of the Terminal Side of an Angle θ\thetaθ In Standard Position Is Given Along with a Restriction on In Standard

An Equation of the Terminal Side of an Angle $\theta$ In Standard Position Is Given Along with a Restriction on In Standard