7-4 Reference Angles

This week I'm going to talk about reference angles. There are several different ways to use a reference angle. They are used with the six functions from the trig chart. Reference angles are similar to fractions that have been reduced. THEY MUST BE BETWEEN 0° AND 90°.

Steps

1. Find the original quadrant and sketch. (For help finding the quadrant you can use the unit circle from section 7-3)

2. Determine if the angle is positive or negative using unit circle methods (for the unit circle see notes on section 7-3)

3. Subtract from 360° or 180° until |Ɵ| is between 0°and 90°. (Keep in mind that since you’re using absolute value the reference angle will never be a negative number.)

EXAMPLE: Find the reference angle for sin 432°

1. For this problem, you must first find a coterminal angle.

432°-360°=72° (This number can be used for step three as well.)

Next you find and sketch the original quadrant. Since 72° is greater than 0° but less than 90°, your sketch would be in quadrant I. It would look like this:

2. You will next determine if the angle is positive or negative using the formula for sin which is sin=y/r. Since the y axis in quadrant I is positive, you have sin=+ve/r. Therefore, you have a positive reference angle.

3. Since 72° is already between 0° and 90° step three is unnecessary.

You would write your final answer like this: sin 432°=sin 72°.

You can check your answer by plugging it into your calculator. If you get the same number for sides of the equal sign, your answer is correct.

--Sarah