Posted by **lindsay** on Monday, April 23, 2012 at 10:17pm.

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

- trigonometry -
**Bosnian**, Monday, April 23, 2012 at 10:54pm
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

- trigonometry -
**Bosnian**, Monday, April 23, 2012 at 11:12pm
¡Ü

mean less than or equal to

## Answer This Question

## Related Questions

- Precalculs - I have no idea how to do these type of problems. -------Problem...
- Trigonometry - 4. Find the exact value for sin(x+y) if sinx=-4/5 and cos y = 15/...
- Trigonometry - Solve for the following equation to the nearest degree if needed ...
- Math - Solving for Trig Equations - Solve the following equation for 0 less than...
- Math - Solving Trig Equations - Solve each equation for o is less than and/or ...
- i lied. very quick calc problem. - f(x) = abs(sin(x)), -pi less than or equal to...
- Parametric equations/Trigonometry - Lattice points - A lattice point is a point ...
- Trigonometry - a. Find the exact value of sin (theta - pi/6) b. Find the exact ...
- calculus - Consider the function f(x)=65x−cos(x)+2 on the interval 0 less ...
- Trigonometry - Solve sin 2x + sin x = 0 for 0 (Less then or equal to) x (Less ...

More Related Questions