Question 165355: Solve 2sin^2x = sinx for all real values in the interval (0,2pi)
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! 2 * sin^2(x) = sin(x)
dividing both sides of equation by sin(x) gets:
(2* sin^2(x))/sin(x) = 1
dividing both sides of eqution by 2 gets:
sin^2(x)/sin(x) = 1/2
since sin^2(x) = sin(x) * sin(x), equation becomes:
(sin(x)*sin(x))/sin(x) = 1/2
which becomes:
sin(x) = 1/2
-----
if sin(x) = 1/2, then x = 30 degrees.
-----
since sin(x) = hypotenuse / y value on the graph, and since hypotenuse is always positive, and since y value on the graph is positive in quadrants 1 and 2, then sin (180-x) = sin(x).
-----
since 180-30 = 150, then x can be either 30 degrees or 150 degrees.
-----
using the calculator to prove the answer is correct.
sin (30) = 1/2
sin (150) = 1/2
-----
calculator confirms logic and answer is good.
|
|
|
