Find the exact value of the indicated trigonometric function of θ.
-$\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 }

Question

Find the exact value of the indicated trigonometric function of θ.
-$\cos \theta = \frac { 21 } { 29 } , \frac { 3 \pi } { 2 } < \theta < 2 \pi \quad$ Find $\cot \theta$
A) $- \frac { 20 } { 21 }$
B) $- \frac { 21 \sqrt { 2 } } { 4 }$
C) $- \frac { 21 } { 20 }$
D) $\frac { 29 } { 20 }$

Quizplus · Accepted Answer

In the fourth quadrant, sine is negative. Using $\sin^2 \theta + \cos^2 \theta = 1$, we find $\sin \theta = -\frac{20}{29}$. Thus, $\cot \theta = \frac{\cos \theta}{\sin \theta} = \frac{21/29}{-20/29} = -\frac{21}{20}$.

Find the Exact Value of the Indicated Trigonometric Function of θ