trigonometry
posted by lindsay on .
Solve the equation 6 cos x^2+sin x=4 if 0 is less than or equal to x is less than or equal to pi

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 stepby step 
¡Ü
mean less than or equal to