Question

Given that sec theta= -37/12, what is the value of cot theta , for pie/2 < theta< pie?

Answer 1

The answer is B. Thank me in the future!

always remember ~Positive Vibes~

Answer 2

Answer:

Option B is correct.

Step-by-step explanation:

Given that

$\sec{\theta}=-\frac{37}{12}$

and the terminal point $\theta$ is in quadrant 2,i.e $\frac{\pi}{2}$

we have to find the value of $\cot \theta$

As in second quadrant $\cos{\theta}$ is negative.

$\cos{\theta}=\frac{1}{\sec{\theta}}=\frac{1}{\frac{-37}{12}}=-\frac{12}{37}$

As in second quadrant all trigonometric functions are negative except $\sin{\theta} \thinspace and\thinspace \csc{\theta}$

$sin{\theta}=\pm\sqrt{1-\cos^2{\theta}}=\pm\sqrt{1-(-\frac{12}{37})^2)}=\pm\sqrt{1-\frac{144}{1369}}=\pm\sqrt{\frac{1225}{1369}}=\frac{35}{37}$

$\cot{\theta}=\frac{\cos{\theta}}{\sin{\theta}}=\frac{-\frac{12}{37}}{\frac{35}{37}}=-\frac{12}{35}$

Option B is correct.