Pre-Calculus Unit 6 Lesson 4: The Unit Circle
Learning Goal: IWBAT find the exact value of the trigonometric
functions using a point on the unit circle, and for integer multiples of
300, 450, 600 in all quadrants.
Homework: Page 378 (#12-28, 46-62, all even)
-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐ Do Now: In a circle of radius of 20 meters, find the measure of the
central angle intercepted by an arc of length 20 meters.
Recall:
Trigonometric Functions
Let t be a real number and let P = (x, y) be the point on the unit circle
that corresponds to t. Since t lies on the unit circle, then t = θ.
sin (θ) =
cos (θ) =
tan (θ) =
csc (θ) =
sec (θ) =
cot (θ) =
Trigonometric Values of π/6 = 30°
Trigonometric Values of 5π/6, 7π/6, 11π/6
When θ = 5π/6, the terminal
side creates an angle of π/6
radians with the x-axis. Note
that the point (√3/2, 1/2),
corresponds with θ = π/6
Since the point P = (x, y) that
corresponds with θ = 5π/6 is
in Quadrant 2, then the point
must be (-√3/2, 1/2).
Since the point P = (x, y) that
corresponds with θ = 7π/6 is
in Quadrant 3, then the point
must be (-√3/2, -1/2).
Trigonometric Values of π/3 = 60°
Trigonometric Values of 2π/3, 4π/3, 5π/3
When θ = 2π/3, the terminal
side creates an angle of π/3
radians with the x-axis. Note
that the point (1/2, √3/2),
corresponds with θ = π/3
Since the point P = (x, y) that
corresponds with θ = 2π/3 is
in Quadrant 2, then the point
must be (-1/2, √3/2).
Since the point P = (x, y) that
corresponds with θ = 4π/3 is
in Quadrant 3, then the point
must be (-1/2, -√3/2).
Trigonometric Values of π/4 = 45°
Find the values of the six
trigonometric functions of π/4 = 45°
Trigonometric Values of 3π/4, 5π/4, 7π/4
When θ = 3π/4, the terminal
side creates an angle of π/4
radians with the x-axis. Note
that the point (√2/2, √2/2),
corresponds with θ = π/4
Since the point P = (x, y) that
corresponds with θ = 3π/4 is
in Quadrant 2, then the point
must be (-√2/2, √2/2).
Since the point P = (x, y) that
corresponds with θ = 5π/4 is
in Quadrant 3, then the point
must be (-√2/2, -√2/2).
The Unit Circle
The Unit Circle
The Unit Circle
Classwork: p. 378 #19 – 27, #45 – 61 (ODD)
Click on the following link to the Pre-Calculus/ Trigonometry Google
Drive Folder:
https://drive.google.com/folderview?
id=0B9CfDiO9B9fNSUVrNkU4cTJ0ZXM&usp=sharing
Click on the following to access the scanned page:
Unit 6: Trigonometric Functions à Lesson 4: The Unit Circle à
Practice: p. 378 #19 – 27, #45 – 61 (Odd)
Be prepared to share your solutions with the class!
Find Values of the Six Trigonometric Functions
Using a Point on Circle
Find Values of the Six Trigonometric Functions
Using a Point on Circle
" 5 2%
$− , − '
Let t be a real number and let # 3
3 & be a point on the unit
circle that corresponds to t.
Find the values of sin t, cos t, tan t, csc t, sec t, and cot t.
Classwork: p. 378 #11 – 17, #75 – 81 (ODD)
Click on the following link to the Pre-Calculus/ Trigonometry Google
Drive Folder:
https://drive.google.com/folderview?
id=0B9CfDiO9B9fNSUVrNkU4cTJ0ZXM&usp=sharing
Click on the following to access the scanned page:
Unit 6: Trigonometric Functions à Lesson 4: The Unit Circle à
Practice: p. 378 #19 – 27, #45 – 61 (Odd)
Be prepared to share your solutions with the class!