How do you find the exact value of cot(arcsin ((-7/13))?

1 Answer
Jun 17, 2018

+-2sqrt(30)/7

Explanation:

it depends on how you define range of arcsin(theta)
1. range of arcsin(theta) = {y|0 < y <= pi/2 , pi < y <=3/2*pi}
The angle of arcsin(-7/13) is at third quadrant.
cot(arcsin(-7/13))=-sqrt(13^2-(-7)^2)/(-7)=2sqrt(30)/7
2. range of arcsin(theta) = {y|-pi/2 <= y <0, 0 < y <= pi/2}
The angle of arcsin(-7/13) is at fourth quadrant.
cot(arcsin(-7/13))=sqrt(13^2-(-7)^2)/(-7)=-2sqrt(30)/7