Reference Angle Calculator

Formulas

The formulas to calculate the reference angle are:

First Quadrant: \(\text{Reference Angle} = \text{Standard Angle}\)
Second Quadrant: \(\text{Reference Angle} = 180^\circ - \text{Standard Angle}\)
Third Quadrant: \(\text{Reference Angle} = \text{Standard Angle} - 180^\circ\)
Fourth Quadrant: \(\text{Reference Angle} = 360^\circ - \text{Standard Angle}\)

What is a Reference Angle?

A reference angle, also known as the related acute angle or principal angle, is the smallest angle between the terminal side of the given angle and the x-axis. It is always positive and less than or equal to 90 degrees.

Example Calculation

Example:

Standard Angle: 135 degrees

Step 1: Determine the quadrant:

The angle 135 degrees is in the second quadrant.

Step 2: Calculate the reference angle:

\[ \text{Reference Angle} = 180^\circ - 135^\circ = 45^\circ \]