Solving Trigonometric Equations: Divide by Cosine

[TbbZz]

Homework Statement

sinx + cosx = 0

Homework Equations

N/A

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.

 

[rocomath]

$$sin x = -\cos x$$

Divide by cosx, what identity do you get?

 

[HallsofIvy]

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.

 

[TbbZz]

Divide by cosx, what identity do you get?

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