1. Lesson Objective: Evaluate trig functions.
Date:
4.2 Notes: The Unit Circle
Lesson Objective: Evaluate trig functions.
CCSS: F-TF Extend the domain of tri­go­no­me­tric functions using the unit circle.
You will need: calculator
This is Jeopardy!: These are the trig inverse functions for sine and cosine.

2. Lesson 1: Trig. Functions The 6 Trig Functions: Name Func­tion
The 6 Trig Functions:
Name
Ab­bre­via­­tions
Func­tion
Func­tions
Sine
sin
y = sin t
Cosecant
csc
csc t = 1/y
y ≠ 0
csc t = 1/
Cosine
cos
x = cos t
Secant
sec
sec t = 1/x
x ≠ 0
sec t = 1/
Tangent
tan
tan t = y/x x ≠ 0
tan t= /
Cotangent
cot
cot t = x/y y ≠ 0
cot t= /

3. Lesson 2: Evaluating Trig Functions
Evaluate the six trigonometric functions at each real number.
A. t = 60°
sin π/3 = y = csc π/3 = 1/y =
cos π/3 = x = ½ sec π/3 = 1/x =
tan π/3 = y/x = cot π/3 = x/y =

4. Lesson 2: Evaluating Trig Functions

5. Lesson 2: Evaluating Trig Functions
Evaluate the six trigonometric functions at each real number.
B. t = - 25π 4 
sin / = y = csc / = 1/y =
cos / = x = sec / = 1/x =
tan / = y/x = cot / = x/y =

6. Lesson 2: Evaluating Trig Functions
Evaluate the six trigonometric functions at each real number.
C. t = 29π 2 
sin / = y = csc / = 1/y =
cos / = x = sec / = 1/x =
tan / = y/x = cot / = x/y =

7. Lesson 3: Domain, Period, Odd and Even Domain: All real numbers – why?
Domain: All real numbers – why?
Range: Any idea?

8. Lesson 3: Domain, Period, Odd and Even Domain: All real numbers
Domain: All real numbers
Range: ≤ y ≤ and ≤ x ≤ 1
-1 ≤ sin t ≤ ≤ cos t ≤ 1

9. Lesson 3: Domain, Period, Odd and Even Period:
Period:
sin(t + 2πn) = sin t cos(t + 2πn) = cos t

10. Lesson 3: Domain, Period, Odd and Even

11. Lesson 3: Domain, Period, Odd and Even

12. Lesson 4: Using a Calculator Evaluate using a calculator. csc π 8
Evaluate using a calculator.
csc π 8
sin(-100°)

13. Evaluate the six trigonometric functions at each real number.
4.2: Do I Get It? Yes or No
Evaluate the six trigonometric functions at each real number.
t = 13π 6
t = 5π
t = - π 3
Evaluate cot 1.5 using a calculator.