# solving trigonometry equations algebraically

• Apr 2nd 2010, 07:22 AM
richie
solving trigonometry equations algebraically
Hello

I am have a problem solving y =3/tan x and y =2sin x algebraically.

I can do it graphically but have to confirm my answer algebraically.

Can anyone point me in the correct direction on how to do this ?

Thanks.
• Apr 2nd 2010, 07:26 AM
e^(i*pi)
Quote:

Originally Posted by richie
Hello

I am have a problem solving y =3/tan x and y =2sin x algebraically.

I can do it graphically but have to confirm my answer algebraically.

Can anyone point me in the correct direction on how to do this ?

Thanks.

I assume find the points of intersection for the two equations given?

If so set them equal:

$\frac{3}{\tan(x)} = 2\sin(x)$

$\frac{3\sin(x)}{cos(x)} - 2\sin(x) = 0$

Multiply both sides by $\cos(x)$

$3\sin(x) - 2\sin(x)\cos(x) = 0$

Factor out sin(x)

$\sin(x)(3-2\cos(x))= 0$

From this we can use the null factor theorem to solve
• Apr 2nd 2010, 08:53 PM
richie
solving trigonometry algebraically
To e^(1*pi)