Introduction to the Unit Circle Angles on the circle

An angle is in standard position when the vertex is at the origin and the initial side lies on the positive side of the x-axis. The ray that forms the initial side of the angle is rotated around the origin with the resulting ray being called the terminal side of the angle.

An angle is positive when the location of the terminal side results from a counterclockwise rotation. An angle is negative when the location of the terminal side results from a clockwise rotation.

Two angles are coterminal if they are in standard position and share the same terminal side. Angles are also coterminal when they share terminal sides as the result of complete rotations. For example, 20 and 380 are coterminal because 380 =

1) Identify which angles ARE in standard position. 2) Determine if the angles are positive or negative. (Only those in standard position) a.b. c.d. e. f.

3) Sketch each of the following angles and draw a coterminal angle. a.30⁰b. 100⁰ c. 220⁰ (Use a positive coterminal angle)d. -45⁰ 4) DO YOU REMEMBER? Label the quadrants on the coordinate plane.

Ordered Pairs on the Unit Circle Warm-Up: Which quadrant does the terminal side of the following angles fall in? 1.75⁰ 2.351⁰ 3.-82⁰ ⁰ ⁰ 6.750⁰ ⁰

Why is it the “unit circle”? (1,0) (-1,0) (0,1) (0,-1) What are the coordinates of the terminal side for each of the following angles? a. 0⁰ b. 90⁰ c. 180⁰ d. 270⁰ e. 360⁰

(1,0) (-1,0) (0,1) (0,-1) Consider 45⁰. What is another positive angle with the same x- coordinate? Same y-coordinate? Negative angle with same x? Angle greater than 360⁰ with same y? 45⁰

(1,0) (-1,0) (0,1) (0,-1) Consider 30⁰. What is another positive angle with the same x- coordinate? Same y-coordinate? Negative x-value? Negative y-value? 30⁰

(1,0) (-1,0) (0,1) (0,-1) Lets reconsider 45⁰. What are the coordinates for the terminal side? (Hint: Consider a special right triangle) 45⁰

Let’s label the unit circle!