Home‎ > ‎PreCalc Review‎ > ‎

5-Unit Circle Trig

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





Showing 0 items
AssignmentDue DateNotes
Sort 
 
Sort 
 
Sort 
 
AssignmentDue DateNotes
Showing 0 items
Ċ
Nikhil Joshi,
Feb 13, 2017, 7:53 AM
Ċ
Nikhil Joshi,
Feb 1, 2017, 6:56 AM
Ċ
Nikhil Joshi,
Feb 28, 2017, 7:53 AM
Ċ
Nikhil Joshi,
Jan 11, 2017, 10:37 AM
Ĉ
Nikhil Joshi,
Jan 9, 2017, 9:08 AM
Ĉ
Nikhil Joshi,
Jan 11, 2017, 10:09 AM
Ċ
Nikhil Joshi,
Jan 17, 2017, 11:50 AM
Ċ
Nikhil Joshi,
Jan 17, 2017, 8:44 AM