Posted by **jess** on Tuesday, December 18, 2007 at 8:02pm.

Im having problems solving this equation:

2sin(x) = cos(x) + 2

I keep getting an imaginary number..:/

- math (trig) -
**drwls**, Tuesday, December 18, 2007 at 8:21pm
2 sin x -2 = cos x = sqrt(1 - sin^2 x)

4 sin^2 x - 8 sin x + 4 = 1 - sin^2 x

5 sin^2 x - 8 sin x + 3 = 0

Let sin x = y

5y^2 -8y +3 = 0

(5y-3)(y-1) = 0

sin x = 1 or 3/5

x = pi/2 (90 degrees) is one solution. There are others as well

- math (trig) -
**drwls**, Tuesday, December 18, 2007 at 8:33pm
It somes from squaring 2sin x - 2.

[2(sin x -1)]^2 = 4(sinx-1)^2

= 4 (sin^2 - 2x +1)= ...

- math (trig) -
**Reiny**, Tuesday, December 18, 2007 at 9:15pm
Jess, don't forget that after you square an equation all answers you obtain must be verified.

for example, the second part to drwls solution was

sinx = 3/5

which produces answers of 36.87º and 143.13º

when these are checked in the original equation, x= 143.13 works but x = 36.87 does not

so x = 90º or x = 143.13º

## Answer this Question

## Related Questions

- trig - 2sin(x)cos(x)+cos(x)=0 I'm looking for exact value solutions in [0, 3&#...
- Math - Solving Trig Equations - What am I doing wrong? Equation: sin2x = 2cos2x ...
- Math - Solving for Trig Equations - For the following equation, why cannot I not...
- math (final trig problem) - Solve for x on the interval [0,π/2): cos^3(2x...
- Precal - I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A...
- Math - Solving Trig Equations - Solve each equation for 0 is less than and equal...
- math (trig) - Find sin(x/2) if sin(x)= -0.4 and 3pi/2 < or equal to (x) < ...
- trig - I do not understand these problems. :S I'd really appreciate the help. ...
- trig - 2sin(4x)[(cos(3/2)x)(cos(5x/2)-sin((15/4)x)]+x can someone simplify this ...
- Math - Solving Trig Equations - Solve each equation for o is less than and/or ...