# Chapter 1: Mathematical Logic and Reasoning

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```					Chapter 6: Trigonometric Identities and Equations

Day                               Subject Matter of the Day
 Lesson 6.1 Graphs of Identities
o Identity: an equation that is true for all values for
which both sides are defined
o Domain: same for both (discontinuities)
o GRAPH: if both sides give the same curve
(But does not show removable)


o One counterexample means no identity
 Problems     Page Examples
1 25        353      6, 9, 11
 Lesson 6.2 Proving Identities
o GRAPH FIRST (to check)
o Methods
1. Manipulate one side only
2
2. Manipulate both sides independently
3. Manipulate with reversible steps
 Problems            Page Examples
1 21 (not 3)       358       1, 6
 Lesson 6.3 Transformations of Graphs of the Circular
Functions
o
o T(h, k) & S(ax,by)
3                   o Amp =          period = 2
o Phase = h       Vertical = k
o Sinusoidal: looks like a sine wave, periodic motion
 Problems     Page Examples
1 21        365      10, 11
4               Ms 6.1 to 6.3
 Lesson 6.4 Formulas for cos()
o
5                   o Compliments & Supplemental
 Problems     Page Examples
1 18        370     5, 9
 Lesson 6.5 Formulas for sin() and tan()
o
6                   o
 Problems        Page   Examples
1 19           375     2, 9
7     Work Day
8     Ms 6.4 to 6.5
 Lesson 6.6 Formulas for cos 2x and sin 2x
o Double Angle:
 sin2x = 2sinx cosx
 cos2x = cos2x – sin2x
 cos2x = 2cos2x – 1
 cos2x = 1 – 2sin2x
o Half-Angles:
9




o Range: dx =
 Problems     Page Examples
1 20         381     5, 12
 Lesson 6.7 Inverse Trigonometric Functions
o Inverse are used to find angles
o DOMAIN:

10               

 Problems     Page Examples
1 25        389       13
 Lesson 6.8 Solving Trigonometric Equations and Inequalities
o Specific Solutions: from the first period
o General Solutions: specific solutions + (period * n)
o Steps:
 Graphical
11                Algebraic
o Inequalities: Test-Point Method: try a point in all
intervals broken up by the zeros of the
function
 Problems     Page Examples
1 22        395       5, 8
12    Work Day
13    Ms 6.6 to 6.8
   Chapter 6 Review
14
o Worksheet
   Test Chapter 6
15
o Test corrections are due two days later

```
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