The steps in finding the reference angles are:
- Find the original quadrant and sketch
- Determine if the angle is positive or negative, using the unit circle methods.
- Subtract the given degrees from rather 360 degrees or 180 degrees until, theta is between 0 degrees and 90 degrees.
Example #1
Express sin 695 degrees in terms of a reference angle.
1) You sketch, then you find what quadrant it is in.
2) Looking back at your unit circle methods, you determine wether the number is positive or negative. The formula for sin is y/r.
3) The number is in the 4th quadrant therefore it is negative.
4) You subtract 695 degrees by 360 degrees, twice.
5) Your final answer is -sin25 degrees.
Example #2
Evaluate!
*When the directions say evaluate, give a number answer from your trig chart, unit circle, or calculator.
Sin 120 degrees
1) You sketch, then you find what quadrant 120 is located in.
2) You determine wether the number is positive or negative, looking back at your unit circle. In this case the number is positive. The formula for solving sin is y/r.
3) You subtract 120 degrees from 180 degrees.
4) You get sin 60 degrees.
5) You have to find your final answer by looking back at your trig chart.
6) Your final answer is the square root of 3pi/2.
