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Accelerated Pre-Calculus Unit 1
Introduction to Trigonometric Functions
Dear Parents,
In this unit, students will be introduced to a basic understanding of trigonometric functions, which will be further
developed upon in Unit 2. Students will apply their understanding of right triangle trig, learned in Geometry, and
apply it to the unit circle. Students will also learn how to graph trig functions along with identifying and
understanding characteristics specific to trig functions.
The main
By the end of the unit, students will be able to…
 Explain what is meant by the radian measure of an angle.
 Define the trigonometric functions in terms of a point on the unit circle.
 Be able to determine the trigonometric values of one of the special real numbers by using the reference
number of that real number.
 Be able to graph a trigonometric function and identify its characteristics.
 Know what is meant by the amplitude, the period, and the phase shift of a trigonometric function.
 Be able to write an equation of a trigonometric function given the characteristics of that function.

Be able to explain why  sin t    cos t   1 is an identity and use it to solve problems.
2
Important Vocabulary
Standard Position
Initial Side
Terminal Side
Coterminal Angle
Reference Angle
2
Unit Circle
Radian
Subtended Arc
Sinusoidal Function
Midline
Amplitude
Period
Frequency
Resources:
Textbook:
Holt McDougal – Advanced Algebra – Unit 5, Modules 10 & 11
Online Digital Access: http://my.hrw.com/
Video Resources - Khan Academy & Learn Zillion:
Understand Radian Measure of an Angle (lesson set) - Learn Zillion Video
Extend Trigonometric Functions to all Real Numbers using Unit Circle (lesson set) - Learn Zillion Video
Explain How Unit Circle Enables the Extension of Trigonometric Functions (lesson set) - Learn Zillion Video
Choose Trigonometric Functions to Model Periodic Phenomena (lesson set) - Learn Zillion Video
Prove the Pythagorean Identity and Use it to Find Trig Values (lesson set) - Learn Zillion Video
Basic Trigonometry (Review of Right Triangle Trig from Analytic Geometry) - Khan Academy Video
Unit Circle Definition of Trig Functions (lesson set) - Khan Academy Video
Graphs of Trig Functions (lesson set) - Khan Academy Video
Trig Identities and Examples (lesson set) - Khan Academy Video
Sample Problems
The Unit Circle
1. Convert 78  to radians.
2
Convert
radians to degrees.
3
7
3. What is the cos
?
6
2.
Find the coordinates of the point where the
terminal side of a 330  angle intersects the unit
circle.
Accelerated Pre-Calculus Unit 1
Introduction to Trigonometric Functions
Graphing Trigonometric Functions
1. Graph the function f(x) = 2 sin x over the restricted domain [ 2 , 2 ].
Then describe the period, midline, amplitude, and frequency.
2. Write an equation to describe the graphed function.
The Pythagorean Identity
1. Michael believes the equation sin A = 1 – cos2 A to be an identity. Why is he mistaken?
2. Given that sin A = ½, what is the value of cos A if angle A lies in the first quadrant of the coordinate plane?
Round your answer to the nearest hundredth.
3.