Solving Trigonometric Equations - 0 to 2pi

[camboguy]

Question 1

sin theta = 2/3 tan theta < 0

sin2 theta = ??


how would i do this?
please help

____
Question 2

solve

2cos^2 theta - cos theta = 1 for 0 <= theta < 2pie


how would i do this one too?

 

[Dick]

The rules of the forum are that you have to at least try the problem before we can really help. But I can help a little, on the first one square both sides and remember, tan(theta)=sin(theta)/cos(theta) and cos^2(theta)=1-sin^2(theta).

 

[bel]

For the first question, you ought to know that $$tan \theta = \frac{sin\theta}{cos \theta}$$ and that $$sin2\theta = 2 sin\theta cos\theta$$. The second question is just a quadratic equation.