# Solving for theta

• Jun 2nd 2011, 01:30 AM
sassysue
Solving for theta
Hello,
I'm not sure how to solve this nor where to start...

question- solve for θ over the specified domain
tanθ= -1/sqr(3)
domain= -180 \leqslant θ \leqslant 180

If anyone can start me off or tell me what to do it'll be appreciated allot

thanks
• Jun 2nd 2011, 02:32 AM
chisigma
Quote:

Originally Posted by sassysue
Hello,
I'm not sure how to solve this nor where to start...

question- solve for θ over the specified domain
tanθ= -1/sqr(3)
domain= -180 \leqslant θ \leqslant 180

If anyone can start me off or tell me what to do it'll be appreciated allot

thanks

Is...

$\displaystyle \tan \theta= \frac{\sin \theta}{\sqrt{1-\sin^{2} \theta}}= - \frac{1}{\sqrt{3}}$ (1)

Set $\displaystyle \sin \theta = x$ and then solve for x...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$
• Jun 2nd 2011, 02:35 AM
Prove It
You should be familiar with similar triangles to be able to solve $\displaystyle \displaystyle \tan{\theta} = \frac{1}{\sqrt{3}}$ for $\displaystyle \displaystyle \theta$, and then evaluate the equivalent angles in the second and fourth quadrants (where the tangent function is negative).