# Thread: Solving For 'X' Using Trigonometry

1. ## Solving For 'X' Using Trigonometry

Hi there!
I am just wondering how you would solve for this?
Solve the equation sin(3x/2) = 1/2 for x E (-pi, pi)

Any help much appreciated,

2. ## Re: Solving For 'X' Using Trigonometry

For what values of $\theta$ do you have $\sin \theta = \dfrac{1}{2}$? You should know the table:

$\begin{matrix}\theta & \sin \theta \\ 0 & 0 \\ \dfrac{\pi}{6} & \dfrac{1}{2} \\ \dfrac{\pi}{4} & \dfrac{\sqrt{2}}{2} \\ \dfrac{\pi}{3} & \dfrac{\sqrt{3}}{2} \\ \dfrac{\pi}{2} & 1\end{matrix}$

Now, in the interval $x \in (-\pi,\pi)$, will you have any other possible values for $\theta$? How can you tell? Once you have all possible values for $\theta$, you have $\theta = \dfrac{3x}{2}$. Solve for $x$. (Hint: you should find three possible values for $\theta$ where $x \in (-\pi,\pi)$).

3. ## Re: Solving For 'X' Using Trigonometry Originally Posted by EbonyJade Hi there!
I am just wondering how you would solve for this?
Solve the equation sin(3x/2) = 1/2 for x E (-pie, pie)Any help much appreciated,
One eats pie. One calculates with the number pi That is $\pi$.

If $\sin(\theta)=\dfrac{1}{2}$ then $\theta=\dfrac{\pi}{6}\text{ or }\dfrac{5\pi}{6}$

4. ## Re: Solving For 'X' Using Trigonometry Originally Posted by Plato One eats pie. One calculates with the number pi That is $\pi$.

If $\sin(\theta)=\dfrac{1}{2}$ then $\theta=\dfrac{\pi}{6}\text{ or }\dfrac{5\pi}{6}$
Or, $\theta = \dfrac{5\pi}{6}-2\pi = -\dfrac{7\pi}{6}$

5. ## Re: Solving For 'X' Using Trigonometry Originally Posted by SlipEternal For what values of $\theta$ do you have $\sin \theta = \dfrac{1}{2}$? You should know the table:

$\begin{matrix}\theta & \sin \theta \\ 0 & 0 \\ \dfrac{\pi}{6} & \dfrac{1}{2} \\ \dfrac{\pi}{4} & \dfrac{\sqrt{2}}{2} \\ \dfrac{\pi}{3} & \dfrac{\sqrt{3}}{2} \\ \dfrac{\pi}{2} & 1\end{matrix}$

Now, in the interval $x \in (-\pi,\pi)$, will you have any other possible values for $\theta$? How can you tell? Once you have all possible values for $\theta$, you have $\theta = \dfrac{3x}{2}$. Solve for $x$. (Hint: you should find three possible values for $\theta$ where $x \in (-\pi,\pi)$).
Awesome thanks SlipEternal!

6. ## Re: Solving For 'X' Using Trigonometry Originally Posted by Plato One eats pie. One calculates with the number pi That is $\pi$.

If $\sin(\theta)=\dfrac{1}{2}$ then $\theta=\dfrac{\pi}{6}\text{ or }\dfrac{5\pi}{6}$

Haha! Thanks Plato! Just realised!
Whoops!!

7. ## Re: Solving For 'X' Using Trigonometry

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