# Trigonometric Equations

1. Jan 8, 2008

### TbbZz

1. The problem statement, all variables and given/known data
sinx + cosx = 0

2. Relevant equations
N/A

3. The attempt at a solution

sinx + cosx = 0

sinx = -cosx
sinx = (+/-) sqrt(sin^2x - 1)
(sinx)^2 = (+/-) sqrt(sin^2x - 1)^2
sinx = sin^2x - 1

Not really too sure what to do from here on.

The answer is 3$$\pi$$/4 and 7$$\pi$$/4.

I appreciate the help, thanks in advance.

2. Jan 8, 2008

### rocomath

$$sin x = -\cos x$$

Divide by cosx, what identity do you get?

3. Jan 8, 2008

### HallsofIvy

Staff Emeritus
Or, since you have gone to all the work of getting to [itex]sin(x)= sin^2(x)- 1[/tex], let y= sin(x) and rewrite it as y^2- y- 1= 0. solve that quadratic equation for y and then solve sin(x)= y.

Last edited: Jan 9, 2008
4. Jan 8, 2008

### TbbZz

Thank you for the assistance, I can't believe I missed that!