Posted by Calvin on Thursday, May 17, 2012 at 4:47pm.
cos ^ 2 ( x ) = 1 - sin ^ 2 ( x )
2 cos ^ 2 ( x ) - sin ( x ) = 1
2 * [ 1 - sin ^ 2 ( x ) ] - sin ( x ) = 1
2 - 2 sin ^ 2 ( x ) - sin ( x ) = 1 Subtract 1 to both sides
2 - 2 sin ^ 2 ( x ) - sin ( x ) - 1 = 1 - 1
- 2 sin ^ 2 ( x ) - sin ( x ) + 1 = 0
Substitute :
sin ( x ) = u
- 2 u ^ 2 - u + 1 = 0
The exact solution are :
u = 1 / 2
u = - 1
cos ( x ) = 1 / 2
cos ( x ) = - 1
x = 30 ° = pi / 6
x = 270 ° = 9 pi / 6 rad
P.S
If you don't know how to solve equation :
- 2 u ^ 2 - u + 1 = 0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
- 2 u ^ 2 - u + 1 = 0
and click option: solve it!
You wil see solution step-by-step
Corection:
sin ( x ) = 1 / 2
sin ( x ) = - 1
would the 3 answers be: pi/6, 5pi/6, 3pi/2
Yes
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