Question

Find the exact values of a) sec of theta b)tan of theta if cos of theta= -4/5 and sin<0

Answer 1

Answer:

$\sec\theta=-\frac{5}{4}$

$\tan\theta=\frac{3}{4}$

Step-by-step explanation:

Since the sine function and cosine function is negative hence, the angle theta must lie in 3rd quadrant.

In 3rd quadrant, tangent and cot functions are positive.

a)

$\sec\theta=\frac{1}{\cos\theta}\\\\\sec\theta=\frac{1}{-4/5}\\\\\sec\theta=-\frac{5}{4}$

b)

$\tan\theta=\sqrt{\sec^2\theta-1}\\\\\tan\theta=\sqrt{25/16-1}\\\\\tan\theta=\sqrt{9/16}\\\\\tan\theta=\frac{3}{4}$