Reference Angles

This week we learned about reference angles. Reference angles are angles that are formed by the terminal ray and the x-axis. All reference angles are acute angles. Reference angles can be formed in each quadrant. There are formulas to determine the reference angle in each quadrant.

In the first quadrant, the reference angle is always equal to theta. To find the reference angle in the second quadrant, you would do the equation, “180-theta”. In the third quadrant, you would the equation, “theta-180”. In the fourth quadrant, you would do the equation “360-theta”.

EXAMPLE PROBLEM: Find the reference angle of an angle that is 193 degrees.

1. First, determine the quadrant in which the angle is in.

2. 193 degrees is in the 3rd quadrant, so I would use the formula "theta-180".

3. 190-180 is equal to 13 degrees.

4. Draw the reference angle to x-axis.

Since theta was positioned in the x-axis, I found the reference angle by using the formula "theta-180". Once I found the reference angle, I formed the angle to the x-axis.

An important note to remember is that reference angles are not formed to the y-axis, but always to the x-axis. There are many things you can do once you find the reference angle. For example, when you draw the reference angle to the x-axis, a special right triangle is formed. From that point, you can figure out special trigonometric identities such as sin, cosine, and tangent.