SOLUTION: tan (sin^-1(x))

Algebra ->  Equations -> SOLUTION: tan (sin^-1(x))      Log On


   

Question 1128160: tan (sin^-1(x))
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
You are given that  

sin%28theta%29 = x   and  theta is between -pi%2F2  and  pi%2F2,      (1)

and they want you calculate  tan%28theta%29.


From (1),  cos%28theta%29 = sqrt%281-sin%5E2%28theta%29%29 = sqrt%281-x%5E2%29 and  cos%28theta%29  is positive in the given interval.


So,  tan%28theta%29 = sin%28theta%29%2Fcos%28theta%29 = x%2Fsqrt%281-x%5E2%29.


Note that  tan%28theta%29 might be positive or negative depending on the sign of "x".


You may often meet such problems in your school years - so memorize this solution and repeat it as a mantra
when you will solve similar problem next time.