Pre-Calculus Honors
Unit 6 Lesson 5
Pre-Calculus Agenda
Objective: Students will be able to find the exact values for
Sine and Cosine to build the unit circle and graph of each
function.
1. Do Now: Review of finding exact value of trig functions
given a radian or angle measure. Do not hand in your Do
Now. We will go over answers.
2. Group Work: Building a table and graph of the Sine and
Cosine functions. After the graph is constructed, use the table
or graph to answer questions in the communication box.
3. Tomorrow: We will be shifting these functions around the
coordinate plane so you want to understand the properties of
the basic function.
Name:
Unit 6 Lesson 5 Do Now.
Evaluate the following functions without using a calculator. (Do not hand in)
1. tan-
p
2
2. sec
23
6
3. sin 
3
4
Pre-Calculus Honors
Unit 6 Lesson 5
Pre-Calculus Honors
Book Reference 4.4
Unit 6 Lesson 5: Unwrapping the Unit Circle (Properties of the Sin and Cosine
Functions)
Objective: ___________________________________________________________
1. Group Practice: Properties of the Sine Function
Unit Circle
Numerical Representation
Evaluate the following without a calculator. You should recognize a pattern so you do
not need to continue evaluating the points by hand.
x
0

6

4

3

2
sinx
x
x
2
3
3
4
5
6

5
3
7
4
11
6
2
sinx
7
6
5
4
4
3
3
2
sinx
x
sinx
Graphical Representation
Graph f(x) = sinx without using a graphing calculator. Find what the x and y scale is on the graph.
Communication
Answer the following questions below.
1. What is the domain and range of the function f(x)?
2.
What is the end behavior of f(x)? Explain.
3.
Is this function even, odd, or neither? Explain.
4.
The sine function is periodic. The sine and cosine function have a period of 2 . Explain what you think the period of a function
means based on the observations in the table and the unit circle. Draw the left side of this function based on these observations.
5.
The amplitude of a function is the height of a wave. Explain what you think the amplitude is of the sine function.
6.
In the next lesson we will be doing graphical transformations of Trig Functions. Explain what you think would be appropriate basic
points to use to shift the sine function.
Pre-Calculus Honors
Unit 6 Lesson 5
2. Group Practice: Properties of the Cosine Function
Unit Circle
Numerical Representation
Evaluate the following without a calculator. You should recognize a pattern so you do
not need to continue evaluating the points by hand.
x
0

6

4

3

2
cosx
x
x
2
3
3
4
5
6

5
3
7
4
11
6
2
cosx
7
6
5
4
4
3
3
2
cosx
x
cosx
Graphical Representation
Graph f(x) = cosx without using a graphing calculator
Communication
Answer the following questions below.
1. What is the domain and range of the function f(x)?
2.
What is the end behavior of f(x)? Explain.
3.
Is this function even, odd, or neither? Explain.
4.
The sine function is periodic. The cosine and cosine function have a period of 2 . Explain what you think the period of a function
means based on the observations in the table and the unit circle. Draw the left side of this function based on these observations.
5.
The amplitude of a function is the height of a wave. Explain what you think the amplitude is of the cosine function.
6.
In the next lesson we will be doing graphical transformations of Trig Functions. Explain what you think would be appropriate basic
points to use to shift the cosine function.