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).
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
