## Getting started

The following page uses inverses trig functions,
and shows you how to solve simple trig equations using the graphs. An example question might be
\[\begin{align}
\text{Find }\theta\hspace{6pt}\text{for }&0\leq\theta\leq360
\\[6pt] \sin(\theta)&=0.5
\end{align}\]
For this page, **I'm going to use degrees**, but the methods are exactly the same if you
were to use radians. See this page
for help converting between degrees and radians.

## Worked Example: using the graphs

Let's take the previously mentioned question:
\[\begin{align}
\text{Find }\theta\hspace{6pt}\text{for }&0\leq\theta\leq360
\\[6pt] \sin(\theta)&=0.5
\end{align}\]
We can simply use the inverse,
\[\theta=\sin^{-1}(0.5)\]
Here, you would use a calculator's \(\sin^{-1}\) function to get
\[\theta = 30^\circ\]
**But this isn't the full answer!** Let's look at the graph for \(\sin(\theta)=0.5\):

*This process might seem long when explained but practice a few times and you'll find it really is pretty quick!*

**(See 2nd example)**
Let's focus on the range we're given: \(0\leq\theta\leq360\) - this region is shaded pink.
Now there's only one solution we don't know. Because of the symmetry in a sine curve, and
our knowledge that it has a **zero at \(\theta=180\)**, we can work out that the other solution
is \(\theta=180-30=150\) as shown below.

**Note:** you don't need to be exact with your curve sketch, you're not reading values off of it, just using it
to help visualise where the solutions lie! We can conclude that
\[\theta=30^\circ\hspace{8pt}\text{or }150^\circ\]

## Worked Example: easy once you know how (1)

This is what it would look like to solve a similar problem with a sketch.