SOLUTION: solve the equation for the solutions in the interval [0,2 pie): tan(x/2)= sin x

Algebra ->  Trigonometry-basics -> SOLUTION: solve the equation for the solutions in the interval [0,2 pie): tan(x/2)= sin x      Log On


   

Question 918947: solve the equation for the solutions in the interval [0,2 pie): tan(x/2)= sin x
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
tan(x/2)= sin x
-----
tan(x/2)= 2sin(x/2)cos(x/2)
sin/cos = 2sin*cos
sin = 2sin*cos^2 = 2sin(1 - sin^2)
Factor out sin(x/2)
sin(x/2) = 0 --> x = 0
--------
1 = 2(1 - sin^2) = 2 - 2sin^2
2sin^2 = 1
sin^2(x/2) = 1/2
x/2 = pi/6, 11pi/6
x = pi/3
===============
--> x = 0, pi/3
-----------
Notice it's the Greek letter pi, not the dessert, pie.
pi, not pie.