Download 10.3C The Unit Circle Objectives: F.TF.2: Explain how the unit circle

10.3C The Unit Circle
Objectives:
F.TF.2: Explain how the unit circle in the coordinate plane enables the extension of
trigonometric functions to all real numbers, interpreted as radian measures of angles
traversed counterclockwise around the unit circle.
F.TF.1: Understand radian measure of an angle as the length of the arc on the unit circle
subtended by the angle.
F.TF.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric
functions.
For the Board: You will be able to convert angle measures between degrees and radians and find the
values of trigonometric functions on the unit circle.
Anticipatory Set:
If you know the measure of a central angle of a circle in radians, you can determine the length s of the
arc intercepted by the angle.
θ
s
s
s = rθ


2π 2r
r
Instruction:
Open the book to page 710 and read example 4.
Example: A tire of a car makes 653 complete rotations in 1 min. The diameter of the tire is 0.65
meters. To the nearest meter, how far does the car travel in 1 second.
θ = 2π ∙ 653 = 1306π
r = 0.65/2 = 0.325
s (in minutes) = 1306π ∙ 0.325 = 424.45π
s (in seconds) = 424.45π/60 = 22 meters
White Board Activity:
Practice: The hour hand on Big Ben’s Clock Tower in London is 14 feet long. To the nearest tenth of a
foot, how far does the tip of the hour hand travel in 1 minute.
θ = 1/60 ∙ 2π = π/30
s = π/30 ∙ 14 = 1.5 feet
Assessment:
Question student pairs.
Independent Practice:
Text: pg. 711 prob. 18, 35, 39, 40.