# Math Help - More trig equations.

1. ## More trig equations.

The first one is
sinx+cosx=0 solve between 0 and 2pi
See I am not sure how to start this one?

The next question is find find for all real values of x

3tanx^2= square root 3 tanx Also the square root only covers 3
So to do this one would I have to square the square root of 3 on one side
Then on the other side do (3tanx^2)(3tan^2x)
Also the x is on the tan not on the exponent.

2. Originally Posted by homeylova223
The first one is
sinx+cosx=0 solve between 0 and 2pi <--- (A)
See I am not sure how to start this one?

The next question is find find for all real values of x

3tanx^2= square root 3 tanx <--- (B)
Also the square root only covers 3
So to do this one would I have to square the square root of 3 on one side
Then on the other side do (3tanx^2)(3tan^2x)
Also the x is on the tan not on the exponent.
to (A):

$\sin(x)+\cos(x)=0~\implies~ \sin(x)=-\cos(x)$ Divide by cos(x)

$\tan(x)=-1$

Use your calculator and the $\tan^{-1}$-mode.

To (B):

$3\tan^2(x)=\sqrt{3} \cdot \tan(x)~\implies~3\tan^2(x) - \sqrt{3} \cdot \tan(x) = 0$ Factor out 3tan(x):

$3\tan(x)\left(\tan(x)-\dfrac1{\sqrt{3}}\right)=0$

A product equals zero if one factor equals zero. Therefore you have to solve for x:

$3\tan(x)=0~\vee~\tan(x)-\frac1{\sqrt{3}}=0$

Use your calculator and the $\tan^{-1}$-mode.