How do you find the exact value for tan (sin^-1(-4/5))?

1 Answer
Mar 10, 2016

tan(sin^(-1)(-4/5))=+-4/3

Explanation:

Let sintheta=(-4/5) ............(A)
where theta=sin^(-1)(-4/5)

Hence as cos^2theta=1-sin^2theta, we have

costheta=sqrt(1-sin^2theta)=sqrt(1-(-4/5)^2 or

costheta=sqrt(1-16/25)=sqrt(9/25)=+-3/5 ............(B)

Dividing (A) by(B), we get

tantheta=+-4/3 or

tan(sin^(-1)(-4/5))=+-4/3