Unit 7: Trigonometry Name ________________________ Lesson 2 – The Trigonometric Functions and the Unit Circle The unit circle is a circle of radius one placed on the x-y coordinate plane. Review:

Unit Circle

Reference Angles

Depending on what quadrant the terminal side lies in, finding the reference angle is just a matter of either subtracting ,180 ,2 ,S Sq or 360q from the angle or subtracting the angle from ,180 ,2 ,S Sq or

360q .

If the angle is greater than 360q (or 2S ) , then find the coterminal angle between 0q and 360q (or corresponding measure if in radians) and use the information above to find the reference angle.

The use of reference angles is a way to simplify the calculation of the values of trigonometric functions at various angles. You can memorize the values of a few simple trigonometric equations, and with reference angles,

you can extend this knowledge of a few equations to many more.

Find the reference angles of the following angles on the unit circle:

1. 135q ________ 2. 270q� ________ 3. 280q ________ 4. 145� q ________

5. 53S _________ 6.

6S ________ 7.

4S

� ________ 8. 83S ________

Due to the periodic nature of the trigonometric functions, the value of a trigonometric function at a given angle is

always the same as its value at that angle's reference angle, except when there is a variation in sign. Because we

know the signs of the functions in different quadrants, we can simplify the calculation of the value of a function at

any angle to the value of the function at the reference angle for that angle.

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