Answer:
[tex]\sec\theta=-\frac{5}{4}[/tex]
[tex]\tan\theta=\frac{3}{4}[/tex]
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)
[tex]\sec\theta=\frac{1}{\cos\theta}\\\\\sec\theta=\frac{1}{-4/5}\\\\\sec\theta=-\frac{5}{4}[/tex]
b)
[tex]\tan\theta=\sqrt{\sec^2\theta-1}\\\\\tan\theta=\sqrt{25/16-1}\\\\\tan\theta=\sqrt{9/16}\\\\\tan\theta=\frac{3}{4}[/tex]
