SOLUTION: If sin (x) = 2/3, then find the value of sin(4x). Domain of x: between 0 and 90 degrees.

Algebra ->  Trigonometry-basics -> SOLUTION: If sin (x) = 2/3, then find the value of sin(4x). Domain of x: between 0 and 90 degrees.      Log On


   

Question 544715: If sin (x) = 2/3,
then find the value of sin(4x).
Domain of x: between 0 and 90 degrees.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
If sin (x) = 2/3,
then find the value of sin(4x).
Domain of x: between 0 and 90 degrees
**
sin(x)=2/3 (Given)
cos^2(x)=1-sin^2(x)=1-4/9=5/9
cos(x)=√5/3
..
sin(4x)=2sin(2x)cos(2x)=2*2sin(x)cos(x)*(cos^2(x)-sin^2(x))
sin(4x)=(4*2/3*√5/3)(5/9-4/9)
sin(4x)=8√5/9*1/9=(8√5)/81