Copy of Reference Angles
- Author:
- Michael Weingarden, Auston B Cron
Associated with every angle drawn in standard position (except quadrantal angles) there is another angle called the reference angle. Basically, any angle on the x-y plane has a reference angle, which is always between 0° and 90° or 0 and π/2. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference. Angles in quadrant I are their own reference angles. (Ref.)
Grab point A, the large red point, and drag it around the circle. You should note the reference angle marked in green. Also, observe the signs of the sine and cosine.
Remember: The reference angle is measured from the terminal side of the original angle "to" the x-axis (not the y-axis).
See Analyze Math Reference Angle for questions.
Do cos θ and sin θ have a maximum value?
In which quadrants is cos θ negative? positive?
In which quadrants is sin θ negative? positive?