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

The cotangent of an angle is defined as the cosine of the angle divided by the sine of the angle. For $t = - \frac { 5 \pi } { 4 }$, this is equivalent to cotangent of $\frac { 3 \pi } { 4 }$ due to the periodicity of trigonometric functions. At $\frac { 3 \pi } { 4 }$, both sine and cosine have the same absolute value but opposite signs, resulting in a cotangent of $-1$.

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 $t = - \frac { 5 \pi } { 4 }$