Posted by lindsay on Monday, April 23, 2012 at 10:17pm.
6 cos ^ 2 ( x ) + sin ( x ) = 4
Then :
6 * [ 1 - sin ^ 2 ( x ) ] + sin ( x )= 4
6 - 6 sin ^ 2 ( x ) + sin ( x ) = 4
- 6 sin ^ 2 ( x ) + sin ( x ) + 6 - 4 = 0
- 6 sin ^ 2 ( x ) + sin ( x ) + 2 = 0
Substitution :
sin ( x ) = u
- 6 u ^ 2 + u + 2 = 0
The exact solutions are :
u = 2 / 3
and
u = - 1 / 2
OR
sin ( x ) = 2 / 3
and
sin ( x ) = - 1 / 2
sin ^ - 1 ( 2 / 3 ) = 0.729728 radians
sin ^ - 1 ( - 1 / 2 ) = - pi / 6 radians
The period of sine function is 2 pi.
If :
0 ¡Ü x
Solution are :
x = 2 n pi + ( - pi / 6 ) =
2 n pi - pi / 6
where n is an integer
P.S.
If you don't know how to solve equation :
- 6 u ^ 2 + u + 2 = 0
Then 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:
- 6 u ^ 2 + u + 2 = 0
and click option: solve it
You will see solution step-by step
¡Ü
mean less than or equal to