# Thread: Trigonometry involving Theta

1. ## Trigonometry involving Theta #2

So my teacher is bad at explaining so I need your help.

1. If cosθ = $\dfrac{1}{3}$ and 0 ≤ 2θ ≤ , find sin θ.

2. Find all θ in the interval [0,2) that satisfy the equation: sinθ = $\dfrac{1}{2}$.
Number 2 is suppose to be:
Find all θ in the interval [0,2) that satisfy the equation: $\sin {\theta} - \sin {\theta} \cot {\theta} = 0$

Tips are kind of helpful, but step-by-step views will surely help in understanding it thoroughly...
Thank You!

2. Originally Posted by meiyukichan
So my teacher is bad at explaining so I need your help.

1. If cosθ = $\dfrac{1}{3}$ and 0 ≤ 2θ ≤ , find sin θ.

2. Find all θ in the interval [0,2) that satisfy the equation: sinθ = $\dfrac{1}{2}$.

Tips are kind of helpful, but step-by-step views will surely help in understanding it thoroughly... if that makes sense.
Thank You!
2.

Keep in mind that saying $\sin{\theta}=\frac{1}{2}$ is the exact same as $\sin^{-1}(\frac{1}{2})=\theta$ which literally says "find the angle $\theta$ whose sine equals $\frac{1}{2}$.

Also, think about the unit circle...where is the sine function positive? You are only going to have two answers on the interval $[0,2\pi)$

3. Originally Posted by elizsimca
2.

Keep in mind that saying $\sin{\theta}=\frac{1}{2}$ is the exact same as $\sin^{-1}(\frac{1}{2})=\theta$ which literally says "find the angle $\theta$ whose sine equals $\frac{1}{2}$.

Also, think about the unit circle...where is the sine function positive? You are only going to have two answers on the interval $[0,2\pi)$

Sorry. Really, really sorry. I posted the wrong question.

It's suppose to be:
Find all θ in the interval [0,2) that satisfy the equation: $\sin {\theta} - \sin {\theta} \cot {\theta} = 0$