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 angle corresponds to an angle in standard position whose terminal side is in the third quadrant, where both sine and cosine are negative. However, since $-\frac{5\pi}{4}$ is equivalent to $ \frac{3\pi}{4}$ when considering coterminal angles (adding $2\pi$ to the angle), and the cotangent of $\frac{3\pi}{4}$ (or $\frac{7\pi}{4}$, which is coterminal with $-\frac{5\pi}{4}$) is $-1$, because both sine and cosine have the same absolute value but opposite signs, making their ratio $-1$.

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