Question

Angle A is in standard position and terminates in quadrant IV. If sec(A) = 4/3 , complete the steps to find cot(A).  Use the identity _____ to find the value of ___(A).

Answer 1

First answer is A.

Second answer is: tan.

Third is answer C. sqrt7/3

Fourth answer is A. -3sqrt7/7

Explanation:

Answer 2

we know that
tan²(A)+1 = sec²(A)--------> tan²(A)= sec²(A)-1
tan²(A)= (4/3)²-1------> tan²(A)=16/9-1-----> 7/9
tan²(A)=7/9
if the angle A is in the IV quadrant
then
tan (A) is negative
therefore
tan (A)=-√(7/9)-----> tan (A)=-√7/3
so
cot (A)=1/tan(A)------> cot (A)=-3/√7----> -(3/7)*√7

the answers are
a) the identity is tan²(A)= sec²(A)-1
b) tan (A)=-√7/3