If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\cot t + \csc t$
A) $- \frac { 1 } { 2 }$

B) $- 2$

C) $2$

D) $\frac { 1 } { 2 }$

E) $- \frac { 5 } { 4 }$

Question

If $\cos t = \frac { 3 } { 5 }$ and the terminal point for t is in quadrant IV, find $\cot t + \csc t$
A) $- \frac { 1 } { 2 }$

B) $- 2$

C) $2$

D) $\frac { 1 } { 2 }$

E) $- \frac { 5 } { 4 }$

Quizplus · Accepted Answer

In quadrant IV, sine is negative. Using $\sin^2 t + \cos^2 t = 1$, we find $\sin t = -\frac{4}{5}$. Thus, $\cot t = \frac{\cos t}{\sin t} = -\frac{3}{4}$ and $\csc t = -\frac{5}{4}$. Therefore, $\cot t + \csc t = -\frac{3}{4} - \frac{5}{4} = -2$.

If cos⁡t=35\cos t = \frac { 3 } { 5 }cost=53​

If $\cos t = \frac { 3 } { 5 }$