Find the cotangent (if it exists) of the real number $t = - \frac { 5 \pi } { 4 }$.
A) $\frac { \sqrt { 2 } } { 2 }$
B) $- 1$
C) 1
D) 0
E) $\cot \left( - \frac { 5 \pi } { 4 } \right)$ does not exist

Question

Quizplus · Accepted Answer

We know that $\cot t = \frac{\cos t}{\sin t}$, so we need to find the cosine and sine of $t = -\frac{5\pi}{4}$. We have $\cos\left(-\frac{5\pi}{4}\right) = \cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2}$ and $\sin\left(-\frac{5\pi}{4}\right) = \sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2}$. Thus, $\cot\left(-\frac{5\pi}{4}\right) = \frac{\cos\left(-\frac{5\pi}{4}\right)}{\sin\left(-\frac{5\pi}{4}\right)} = \frac{-\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}} = \boxed{-1}$.

Find the Cotangent (If It Exists) of the Real Number t=−5π4t = - \frac { 5 \pi } { 4 }t=−45π​

Find the Cotangent (If It Exists) of the Real Number $t = - \frac { 5 \pi } { 4 }$