7-4 Reference Angles

This week I am going to teach you how to find reference angles. It only takes three easy steps.
Steps:
1. You have to find the original quadrant (using your unit circle) and sketch.
2. Then you must find out if the angle is positive or negative by using your unit circle. *Use the following formulas to determine positive or negative: sin=y/r, csc=r/y, cos=x/r, sec=r/x, tan=y/x, and cot=x/y*(r is always 1)
3. Lastly, you subtract the angle measure by 360 degrees or 180 degrees until the absolute value of theta is in between 0 degrees and 90 degrees.
Examples:
1. sin 128 degrees 1. It is in quadrant II because 128 degrees is in between 90 degrees and 180 degrees.
2. The formula for sin is y/r, so you get (y/r)= -/1. This gives you a negative answer.
3. Then you do 128 degrees- 180 degrees. This gives you -51 degrees.
The answer is –cos 51 degrees. Remember when you put the answer to step number three in your final answer, you take the absolute value of that number.
Now you know how to find reference angles.
-Braxton-