Periodic Functions and Trigonometry

Review: Special Right Triangles

30o60o45o45o

13-2Angles & the Unit CircleDay 1Todays Objective:I can work with angles in standard position.

Angle on coordinate plane in standard position:

Vertex on originOne ray of angle is on positive x-axisTerminal sideInitial side+ The blue arrow is fixed to the x-axis. Turn the red arrow counterclockwise about the origin.

If the red arrow contains one of the points when it stops, which point would create the angle with the greatest measure? Explain your reasoning(0, 1), (2, 2), (-3, 3), (-1, 0), or (5, 5)

What are the measures of each angle?

Sketch each angle in standard position

Coterminal anglesangles that have the same terminal side

Review: Special Right Triangles

30o60o45o45o

p. 835:1-7 odds p. 840:7-25 odds, 64-66

Angles & the Unit CircleDay 2Todays Objective:I can find the coordinates of points on the unit circle.WE LOVE MATH!!xy(1, 0)(0, 1)(-1, 0)(0, -1)1

SOH CAH TOA

Unit Circle: Radius = 1

Always draw a right trianglewith one leg on x-axis8Special Right Triangles

30o60o45o45oxy(1, 0)(0, 1)(-1, 0)(0, -1)Angle: 30o 1

30oxy(1, 0)(0, 1)(-1, 0)(0, -1)Draw a right triangle with one leg on x-axisAngle: 60o 1

60o

1060oxy(1, 0)(0, 1)(-1, 0)(0, -1)Angle: 120o 1

120oxy(1, 0)(0, 1)(-1, 0)(0, -1)Draw a right triangle with one leg on x-axisAngle: 45o 1

45o

11xy(1, 0)(0, 1)(-1, 0)(0, -1)Points on the axis

Complete Unit Circle12Find the exact value of trigonometric function.

xy(1, 0)(0, 1)(-1, 0)(0, -1)Complete Unit CircleWS Angles & the Unit Circle