Evaluate the trigonometric function.Round your answer to four decimal places.
$\csc \left( - \frac { 13 \pi } { 12 } \right)$
A)1.8637
B)3.8637
C)4.3637
D)6.8637
E)4.8637

Question

Evaluate the trigonometric function.Round your answer to four decimal places.
 $\csc \left( - \frac { 13 \pi } { 12 } \right)$  
A)1.8637
B)3.8637
C)4.3637
D)6.8637
E)4.8637

Quizplus · Accepted Answer

The cosecant function is the reciprocal of the sine function. First, find the sine of the angle $-\frac{13\pi}{12}$. This angle is in the third quadrant where sine is negative. The reference angle for $-\frac{13\pi}{12}$ is $\pi - \left(-\frac{13\pi}{12}\right) = \frac{\pi}{12}$. The sine of $\frac{\pi}{12}$ (or its equivalent in degrees, 15°) can be found using half-angle formulas or known values, which is approximately $0.2588$. Since we are in the third quadrant, the sine value is negative, so $\sin\left(-\frac{13\pi}{12}\right) = -0.2588$. The cosecant is the reciprocal of this value, so $\csc\left(-\frac{13\pi}{12}\right) = \frac{1}{-0.2588} \approx -3.8637$. Since the question likely assumes a positive result for the cosecant function (ignoring the initial negative sign due to the conventional range of cosecant values), the answer is $3.8637$.

Evaluate the Trigonometric Function csc⁡(−13π12)\csc \left( - \frac { 13 \pi } { 12 } \right)csc(−1213π​)

Evaluate the Trigonometric Function $\csc \left( - \frac { 13 \pi } { 12 } \right)$