Download Chapter 4 Newsletter - Summit School District

PreCalc/Trig-Chapter 4
E-mail:
Skills/Concepts-In this chapter, you will find the values of coordinates of key points on the unit circle
and see how they can be used to find the values of sine and cosine for any angle. You will generate parent
graphs for sine and cosine and use them to sketch various transformations. You will define other
trigonometric functions in terms of sine and cosine. You will also model situations using periodic functions.
Guiding Questions- What does the unit circle tell you? How do you create a “wave” function? How do
you shift trigonometric functions?
Vocabulary/Key Ideas
Angles and Coordinates in the Unit Circle
Sine and Cosine in the Unit Circle
The Fundamental Pythagorean Identity
Using Right Triangles to Find Trigonometric
Ratios
Graphs and Transformations of Sine and Cosine
The Five-Point Method for Graphing Sine and
Cosine
The Reciprocal Trig Functions
Date
Book
Learning Target
Section
4.1.1
4.1.2


Recall the special angles in a unit circle.
Find the coordinates of the special angles in a unit
circle.

Learn how sine and cosine can be viewed in terms of the
unit circle.
Develop the Fundamental Pythagorean Identity.
Use the unit circle, the Fundamental Pythagorean
Identity, and right triangles, to find the values of
trigonometric functions.
Generate the graphs of sine and cosine using the unit
circle.
Find the domain, range, and intercepts for the sine and
cosine graphs.
Use shifts and vertical stretches to graph and find the
equations of sinusoidal functions.
Use the 5-point method to sketch graphs.



4.1.3
Other Trigonometric Functions in the Unit Circle
Simplifying Complex Fractions
Angular Frequency and Period
The General Sine Function
The Three Pythagorean Identities
Verifying Identities
Modeling with Periodic Functions
Graphical Addition


4.1.4

Home Practice
4-7 to 4-14
4-24 to 4-31
4-38 to 4-46
4-53 to 4-57
4-59 to 4-61
Quiz

4.2.1


Be introduced to the reciprocal trig functions: cot, sec,
and csc.
Find values for these functions using the unit circle and
a calculator.
4-70 to 4-78

4.2.2
4.2.3




4.2.4
4.3.1
4.3.2





Simplify trig expressions by rewriting the functions in
terms of sine and cosine.
Find special angles for trig ratios from the unit circle.
Practice stretching a sine or cosine graph horizontally.
Learn about angular frequency and its relationship to
period.
Derive the other two Pythagorean identities
(sin²θ + cos²θ = 1 has already been done).
Verify trig identities.
Model a situation using sinusoidal curves.
Graph a sum by adding corresponding coordinates.
Observe that y = sin x + cos x is sinusoidal.
Find the period and estimate the amplitude of y = sin x
+ cos x.
4-84 to 4-91
4-98 to 4-101
4-103 to 4-106
4-111 to 4-116,
and 4-118
4-123 to 4-130
4-137 to 4-142
Team Test
Chapter 4 Review Assignment
Test
Free Math Tutoring
Tuesday 3:00 to 4:30 Ms. Guevara Room 2331
Wednesday 3:00 to 4:30 Ms. Guevara Room 2331
Thursday 3:00 to 4:30 Mr. Nicoletti Room 2334
Closure Problems