Here’s a secret that math tutors keep to themselves: Sometimes, the fanciest math skills are actually the simplest ones! Like the ultra-mysterious ** Reference Angle**! Sounds pretty impressive, no?

But Reference Angles are actually one of the easiest things to define. Let’s draw a graph and an **acute angle** (an angle less than 90) and an **obtuse angle **(an angle that is greater than 90):

The **Reference Angles **are the measurement of degrees from the shortest distance between the *terminal line* to the *X-axis*.

For an *acute angle*, it is very simple. It is just the degrees.Inn this case, it is __45°____. __

Fort an *obtuse angle*, it is a little trickier. The terminal line is actually **closest **to the x-axis on the OPPOSITE side of the angle. In this case, it would be this:

We know the degree measurement is 70° because the angles that make up a straight line through the y-axis is 180°. We just subtract 110° from 180° to get the **REFERENCE ANGLE**!

If this doesn’t make sense, you can get math homework help from a geometry expert.

***Please note that even though the **Reference Angle **is on the negative side of the x-axis, **it is always positive.**

***Also, unless the *terminal side of the angle is on the y-axis* to form a *right angle*, the **Reference Angle** will always be *acute*!!!

In other words, **Reference Angle **≤ **90°**

Here is the largest Reference Angle possible:

It is *right angle *with a measurement of 90°

***We can use Reference Angles to calculate the functions of angles, like *sine, cosine*, and *tangents.* It’s basically a cool shortcut: the *sin(70) and sin(110) are the same* because they have the same Reference Angle!