Important Concepts for This Unit
Many phenomena in nature are cyclical, such as the seasons, the tides, and sound, The sinusoidal functions defined by right triangles can be extended to circles and are vital in understanding any phenomena that repeats over some interval. In this unit we will learn how the sine, cosine, and tangent functions can be used to model cyclical phenomena. The standards that will be assessed in this chapter are
u5.3 TRIGONOMETRIC GRAPHS
Topic, Focus, and Exercises

u5.1  THE
UNIT CIRCLE
 Finding the reference number for a given real number.
 Using reference numbers to find terminal points.
Core Exercises: 1, 8, 22, 33, 39, 57, 59
Recommended: 1, 4, 8, 10, 14, 18, 22, 24, 33, 35, 39, 42, 53, 57,
59, 60

u5.2  TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS
 Computation of the trigonometric functions, given the
terminal point of a real number.
 Properties of the trigonometric functions, including
their domains, and parity based on the quadrant of the terminal
point.
 The Pythagorean and reciprocal identities of the
trigonometric functions.
Core Exercises: 2, 11, 19, 28, 46, 53, 66, 80, 83
Recommended: 2, 4, 7, 11, 15, 19, 22, 28, 31, 37, 44, 46, 51, 53,
61, 66, 72, 76, 80, 83

u5.3 TRIGONOMETRIC
GRAPHS
 The graphs of sine and cosine, their
periodicity, and their transformations.
 Sine and cosine curves with variable
amplitudes.
Core Exercises: 1, 16, 27, 32, 48, 61, 69, 75, 80, 89
Recommended: 1, 3, 8, 12, 16, 20, 27, 32, 34, 42, 48, 51, 55, 61,
63, 69, 72, 75, 80, 82, 86, 89

u5.4 MORE TRIGONOMETRIC GRAPHS
 The graphs of tangent, cotangent, secant, and cosecant,
their periodicity, and their transformations.
Core Exercises: 7, 18, 24, 27, 50, 62
Recommended: 2, 5, 7, 10, 18, 19, 24, 27, 34, 38, 44, 50, 57, 62,
64

u5.5 INVERSE TRIGONOMETRIC FUNCTIONS AND THEIR
GRAPHS
 Defining the inverse trigonometric functions.
 Evaluating the inverse trigonometric functions.
 Graphing the inverse trigonometric functions.
Also look at u7.4  Basic Trigonometric equations.  Solving linear and quadratic trigonometric equations.
 Using identities to put trigonometric equations into linear or quadratic form.
Core Exercises u5.5: 2, 12, 21, 37, 48, 57
Recommended u5.5: 2, 4, 7, 12, 12, 20, 21, 30, 37, 41, 48, 55, 57

u5.6 MODELING HARMONIC
MOTION
 Understanding the meanings of amplitude,
period and frequency, and determining them from formulas
 Understanding the physical meaning of a
horizontal shift in formulas
Core Exercises: 2, 9, 21, 34, 45, 63 Recommended: 2, 4, 5, 9, 15, 19, 21, 25, 34, 36, 40,
45, 49, 63


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