Expert: Ahmed Salami - 10/24/2009

Question
I need help with this problem, please:
Solve the equation:  sin x - 2 sin x cos^2 x = 0, finding all solutions in the interval [0, 360degrees).  Provide exact values of the solutions and state them in degrees.  Thank you!

Answer
Hi Cindy,
sinx - 2sinx.cos²x = 0
sinx(1 - 2cos²x) = 0
So, either sinx = 0 or 1 - 2cos²x = 0
For sinx = 0
x = 0°, 180° or 360°
For 1 - 2cos²x = 0
2cos²x = 1
cos²x = 1/2
cosx = √(1/2)
    = ± 1/√2
For cosx = 1/√2
x = 45° or 315°
For cosx = -1/√2
x = 135° or 225°
Therefore, the complete solution is
x = 0°, 45°, 135°, 180°, 225°, 315° or 360°

Regards