MATH SOLVE

3 months ago

Q:
# 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 ____ (choices are sin^2(A) + cos^2(A) = 1, tan^2(A) + 1 = sec^2(A), 1 + cot^2(A) = csc^2(A) ) to find the value of __(A).

Accepted Solution

A:

Answer:tan²A +1 = sec²A; cotA = -(3√7/7); A = 311.41°
Step-by-step explanation:secA = 4/3
sec²A = 16/9
Use the identity tan²A +1 = sec²A
tan²A = sec²A - 1 = 16/9 - 1 = 7/9
cot²A = 1/tan²A = 9/7
We are in the fourth quadrant, so the cotangent is negative.
cotA = -√(9/7) = -3/√7 = -(3√7/7)
tan A = 1/cotA = -√7/3
A = -48.59° = 311.41°