Thread: Trigonometry involving Theta

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

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

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



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

Originally Posted by meiyukichan

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

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

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


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

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

Originally Posted by elizsimca

2.

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

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

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: $\displaystyle \sin {\theta} - \sin {\theta} \cot {\theta} = 0$