Download PCH Notes 4.2

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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.
Lesson 1: Trig. Functions
The 6 Trig Functions:
AbbreName via- Function
Name
tions
Sine
sin
Abbreviations
Functions
y = sin t Cosecant csc csc t = 1/y
y≠0
Cosine cos x = cos t Secant
csc t = 1/
sec sec t = 1/x
x≠0
sec t = 1/
Tangent tan tan t = y/x Cotangent cot cot t = x/y
x≠0
tan t= /
y≠0
cot t= /
Lesson 2: Evaluating Trig Functions
Evaluate the six trigonometric functions at each
real number.
A.
t = 60°
sin π/3 = y = 3
cos π/3 = x = ½
tan π/3 = y/x =
2
csc π/3 = 1/y =
sec π/3 = 1/x =
cot π/3 = x/y =
Lesson 2: Evaluating Trig Functions
Lesson 2: Evaluating Trig Functions
Evaluate the six trigonometric functions at each
real number.
B.
25π
t=4
sin / = y =
cos / = x =
tan / = y/x =

csc / = 1/y =
sec / = 1/x =
cot / = x/y =
Lesson 2: Evaluating Trig Functions
Evaluate the six trigonometric functions at each
real number.
C.
t=
29π
2

sin / = y =
cos / = x =
tan / = y/x =
csc / = 1/y =
sec / = 1/x =
cot / = x/y =
Lesson 3: Domain, Period, Odd and Even
Domain: All real numbers – why?
Range: Any idea?
Lesson 3: Domain, Period, Odd and Even
Domain: All real numbers
Range: -1 ≤ y ≤ 1 and
-1 ≤ x ≤ 1
-1 ≤ sin t ≤ 1
-1 ≤ cos t ≤ 1
Lesson 3: Domain, Period, Odd and Even
Period:
sin(t + 2πn) = sin t
cos(t + 2πn) = cos t
Lesson 3: Domain, Period, Odd and Even
Lesson 3: Domain, Period, Odd and Even
Lesson 4: Using a Calculator
Evaluate using a calculator.
A. csc
π
8
B. sin(-100°)
4.2: Do I Get It? Yes or No
Evaluate the six trigonometric functions at each
real number.
13π
1. t =
6
2. t = 5π
π
3. t = 3
4. Evaluate cot 1.5 using a calculator.