# Finding the general form....

#### Qwertyuiop23

Today I was having a bit of a nostalgia moment when I came across an old problem then when I tried to solve it...well lets say it was harder than it seemed.

Anyway the equation was:

$$\displaystyle sin(3x) + cos(x) = 0$$

And it asked you to find the general form of the solution...

I have tried compound, double angle formulas but to no avail. I can graph it and find some solutions but not how to find a general form equation? Can someone please shoe me how to solve it?

Cheers
Lance

EDIT:: Changed the - to a plus +

#### sa-ri-ga-ma

Today I was having a bit of a nostalgia moment when I came across an old problem then when I tried to solve it...well lets say it was harder than it seemed.

Anyway the equation was:

$$\displaystyle sin(3x) + cos(x) = 0$$

And it asked you to find the general form of the solution...

I have tried compound, double angle formulas but to no avail. I can graph it and find some solutions but not how to find a general form equation? Can someone please shoe me how to solve it?

Cheers
Lance

cos(x) = -sin(3x) = cos(π/2 + 3χ)

π/2 + 3x = 2nπ + or - ( x)

Now solve for x .

why 2n*pi?

#### BobBali

Trig

Sin (3x) + Cos (x) = 0

Cos(x) = -Sin(3x)
Divide by Cos(x)

- Sin(3x)/Cos(x) = 1
* identity Sinx/Cosx = Tanx

-Tan(2x) = 1

Tan(2x) = -1

2x = Tan^-1 (-1)

Therefore, x = -22.5

#### sa-ri-ga-ma

why 2n*pi?
If cos(x) = 1/2, then x = either 30 degrees or 330 degrees.

In general, n*360 + or - (30).

This is the general solution.