Need help with trigonometric equations! 10pts!

could you please explain how to solve:

sin2(theta)= -(root3)/2

thanks in advance

Hello

Either you know the main values of sin and cos, or you take your calculator

You should memorize the tavle that gives sin and cos of 0°, 30°, 45°, 60°, 90°

But if you don't know you take your calculator

On your calculator, type

3==> √ ==> / ==> 2
then find the opposite ( + ==> -)
Then inv ==> sin ==> you read - 60° = 300°

You must know ( look at the triginometric circle ) that there are two angles that have the same sine

they are θ and (π - θ)

Then 180° -(-60°) = 240° is also a solution.

Do not forget that 240° and 300° are not θ but 2θ

So, the solutions for θ are 120° and 150°

Here is the trigonometric circle :

http://img252.imageshack.us/img252/7296/…

You must always check your solutions

120° x 2 = 240° ==> Calc. 240 ==> sin==> you read -0.866 which is -√3/2
150° x 2 = 300° ==> Calc. 300 ==> sin==> you read -0.866 which is -√3/2

These two answers are right !

Hope it helps

Bye !