Trigonometry involving Theta

**meiyukichan** · Nov 30th 2008, 05:38 PM

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!

**elizsimca** · Nov 30th 2008, 08:20 PM

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 $[0,2\pi)$

**meiyukichan** · Nov 30th 2008, 08:34 PM

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

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