MATH 1113 PreCalculus

Day #2, Part II
Reference Angles

For any angle on the unit circle, its corresponding Reference Angle is simply the (positive) acute angle between the terminal side of the angle and the x-axis.

From our definitions of the trig functions of arbitrary angles, it is clear that the absolute value of the trig function of any angle is equal to the trig function value of the reference angle.  In other words, by looking at the reference angle, you can figure out the value of the trig function of the angle, up to a minus sign, and then you can look at the quadrant to determine the sign of the value.

So the key to the game becomes determining the quadrant of the terminal side of any angle, then going up or down (working off of 0 or pi, or 0 or 180 degrees) to the x-axis to find the reference angle.

Examples:

A common mistake made when you first start calculating trig values is to accidentally draw reference angles over to the y-axis.

Remember: The Reference Angle is always between the terminal side and the x-axis.

Here is a Java "reference angle" calculator.

http://www.analyzemath.com/Calculators/Reference_Cal.html

Sort of cute, but I hope you don't need it.

Here's a better practice applet:

http://colalg.math.csusb.edu/~devel/precalcdemo/rttriangle/src/angles/angles.html

(Scroll all the way to the bottom)

Examples:

Page Last Modified: 10 March, 2007

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