1. +

2. + Bellwork

3. + Objectives You will be able to use reference angles to evaluate the trig functions for any angle. You will be able to locate points on a unit circle and use symmetry to locate other points.

4. + Vocabulary Reference Angle (with examples)

5. + Reference Angles To find a reference angle: Begin by visualizing the angles, and the quadrant in which it terminates. Figure out the distance from the terminal side to the x-axis. Here are some rules to figure out how to calculate the reference angle, based on the original angle:

6. + Take it to the UNIT CIRCLE ON THE UNIT CIRCLE OLNY X = Cos Y = Sin Tan = Y/X KFC

7. + Reference Angles Then, you can calculate the sine, cosine, tangent, etc. (based on what the problem is asking), by calculating the same trig ratio of the reference angle. Make sure the sign is right, based on what quadrant you’re working in. Quadrant 1: All are Positive (both) Quadrant 2: Sine is Positive (y) Quadrant 3: Tangent is Positive (neither) Quadrant 4: Cosine is Positive (x) ASTC: All Students Take Classes

8. + Reference Angles Here is an example problem: Figure out the reference angle. Determine which quadrant you’re in: 4 th quadrant Calculate sin, cos, and tan of the reference angle. Change the signs. (ASTC – Cosine is positive)

9. + Reference Angles Practice Using reference angles, evaluate sin θ for each of the following angles. θ = 135 θ = 300 θ = -45

10. + Symmetry Any time we figure out a point on the unit circle, we can then figure out three other points, just based on symmetry! Remember which coordinate values (x and y) are positive in negative in the different quadrants. Example: we have the point, which is on the unit circle. Determine which quadrant it’s in, and using symmetry, calculate three other points. Solution: this is in the 3 rd quadrant, so we can use the unit circle to the right to find three other points.

11. + Symmetry Practice We know that is a point on the unit circle. Using symmetry, find three other points. Because x is negative, this point must be in the 2 nd quadrant. These points must also be on the unit circle. 3 rd Quadrant…4 th Quadrant…1 st Quadrant…

12. + Homework p. 539, #31-41 odd, 47-54 all p.550, #19-22 all Due TOMORROW