Posted by **Calvin** on Thursday, May 17, 2012 at 4:47pm.

solve 2cos^2x-sinx=1, 0 < or equal to x < 2pie

- trig -
**Bosnian**, Thursday, May 17, 2012 at 5:33pm
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

- trig -
**Bosnian**, Thursday, May 17, 2012 at 5:34pm
Corection:

sin ( x ) = 1 / 2

sin ( x ) = - 1

- trig -
**ky**, Thursday, May 17, 2012 at 5:43pm
would the 3 answers be: pi/6, 5pi/6, 3pi/2

- trig -
**Bosnian**, Thursday, May 17, 2012 at 6:00pm
Yes

## Answer This Question

## Related Questions

- math - the problem is 2cos^2x + sinx-1=0 the directions are to "use an identity ...
- Trig - Verify the identity: tanx(cos2x) = sin2x - tanx Left Side = (sinx/cosx)(...
- MATHS - Solve the following equations if 0<x<2pie (those are 'less than or...
- Trig....... - I need to prove that the following is true. Thanks (2tanx /1-tan^x...
- trig - find the exact solutions 2cos^2x+3sinx=0 the way it stands, that is a "...
- math - solve each equation for 0=/<x=/<2pi sin^2x + 5sinx + 6 = 0? how do ...
- Math - Solving Trig Equations - Solve each equation for 0 is less than and equal...
- Trig Help - Prove the following: [1+sinx]/[1+cscx]=tanx/secx =[1+sinx]/[1+1/sinx...
- Calculus - PLZ show work, find the rieman sum of 6 intervals of sinx from (0,...
- trig - please help me with some questions I skipped on a review for our test ...

More Related Questions