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Chapter 5
Trigonometric Functions

Section 5.1 introduces angles and angle measure.

What is the formula for the circumference of a circle with radius "r"?
What is the formula for the circumference of a circle with diameter "d"?
What is arc length?
How is arc length related to radian measure?
What is a radian?
How is degree measure related to radian measure?
How can you convert back and forth between degree measure and radian measure?
What is the formula for arc length?  Be sure you know what each variable in the formula stands for.
You will need to know the meaning of the following terms:  Initial side, terminal side, central angle, quadrant, standard position, coterminal, positive angle, negative angle, right, acute, obtuse, complementary, supplementary.

What is the difference between angular velocity and linear velocity?
How can you convert between the two types of velocity?

Section 5.2 introduces the unit circle.

What is the unit circle?
What is the wrapping function?
How are the Trigonometric Functions defined on the unit circle using the wrapping function?

There are some commonly used angles shown at the top of page 400. 

• You will need to know the measures of these angles in both degrees and radians. 

• You will need to be able to locate these angles, and integer multiples of these angles, on the unit circle.

• You will need to be able to determine exact values of sine, cosine, tangent, cosecant, secant, and cotangent for these angles and for integer multiples of these angles.
   

What do the graphs of the six trig functions look like?

• You will need to be able to sketch each graph through one period by hand without any aids
• You will need to be able to locate zeros, turning points, asymptotes, etc. by hand.
• Which of these functions are even and which are odd?  Think about the implications of this.
• How is the graph of y = sec x related to the graph of y = cos x ?  Why do these relationships make sense?
• How is the graph of y = csc x related to the graph of y = sin x ?  Why do these relationships make sense?
• How is the graph of y = cot x related to the graph of y = tan x ?  Why do these relationships make sense?

Section 5.3 covers applications of right triangles.

• You will need to memorize the Pythagorean Theorem.
  Be sure you know what each term stands for.

• What is a Pythagorean triple?

• How can you use a right triangle to define the sine, cosine, and tangent?

• How can you use the sine, cosine, or tangent to determine missing measures of a right triangle?

• How do you know which function to use (sine, cosine, or tangent)?

• How can you use a right triangle to solve a story problem?

Section 5.4 introduces properties of trig functions.

• There are 9 basic trig identities listed as Theorem 1 on page 418.  Memorize them and be able to explain why each is true.

• You should be able to determine the sign of each trig function according to the quadrant of the corresponding circular point.

• How can you tell by the graph of a function whether or not it is periodic?

• How can you find the period of a function from its graph?
• How can you use the period of a function to determine function values?
• How can you find the amplitude of a function from its graph?
• What is the relationship between the unit circle and the right triangle definitions of the trig functions?
• What is a reference triangle?
• What is a reference angle?
• How are reference angles and reference triangles used to determine exact values of trig functions?

Section 5.5 deals with using sine and cosine to model periodic behavior.

• You will need to know how to model periodic behavior using a formula of the form
   f(x) = A cos[ B(x+C) ]+D or of the form f(x) = A sin[ B(x+C) ]+D . 

  • What does A stand for? 

    • How can you determine A from a table of values?

    • How can you determine A from a graph?

  • What does B stand for?

    • How can you determine B from a table of values?

    • How can you determine B from a graph?

  • What does C stand for?

    • How can you determine C from a table of values?

    • How can you determine C from a graph?

  • What does D stand for?

    • How can you determine D from a table of values?

    • How can you determine D from a graph?

• How can you determine the period of the sum of two periodic functions using the graph?  Using the formula?

Section 5.6 introduces inverse trig functions.

This would be a good time to go back and review inverses. 
    What are inverse functions?
    How can you determine a formula for the inverse of a function?
    How is the graph of a function related to the graph of its inverse?
    What does one to one mean?
    What is the horizontal line test?
    How can you tell if a function will have an inverse or not?

What is an inverse trig function?
What is an inverse trig function used for?

Fill in the table with information about inverse trig functions .

• You will need to understand the trig - inverse trig function identities listed in this section in the bluish/green boxes. 
• Know how and when to draw a triangle to work with compositions of trig and inverse trig functions.