Question

Find the exact value of sec (theta) if cot (theta) = -2 and the terminal side of theta lies in quadrant IV.

Answer 1

We know that
sec (theta)=1/cos (theta)

cot (theta) = -2
cot (theta)=cos (theta)/sin (theta)
cos (theta)/sin (theta)=-2----> squaring-----> cos² (theta)/sin² (theta)=4
remember that
sin²(theta)+cos²(theta)=1
sin² (theta)=1-cos² (theta)
substitute
 cos² (theta)/[1-cos² (theta)]=4
cos² (theta)=4*[1-cos² (theta)]-----> cos² (theta)+4 cos² (theta)=4
5*cos² (theta)=4-----> cos² (theta)=4/5----> cos (theta)=2/√5
cos (theta)=(2√5)/5-----> is positive  (IV quadrant)
sec (theta)=1/cos (theta)----> √5/2

the answer is
sec (theta)=√5/2

Answer 2

Answer:

B

Step-by-step explanation: