Algebra I: Lesson Plan * 9/29/2006

Section 3-2







Section 3-3







Section 3-4

PreCalculus: Lesson Plan * 9/29/2006

No Quickstart, study for test.

Chapter 5 Test

Lesson
Review Solving Right Triangles
p.361 #8
To solve a right triangle means to find the measure of each angle and the length of each side.
We do this using the Pythagorean Theorem and right triangle trigonometry.

6.1 Law of Sines
I. Introduction
To solve an oblique triangle, a triangle with no right angles, we need to be given at least one side and then any other two parts of the triangle.
We can use the Law of Sines or the Law of Cosines.
Today we learn about the Law of Sines.

Law of Sines
For any triangle ABC with opposite sides a, b, and c







II. The Ambiguous Case (SSA)
See p. 430 of the textbook for illustrations
If two sides and one opposite angle are given, three possible situations can occur:
(1) no such triangle exists, (2) one such triangle exists, or (3) two distinct triangles may satisfy the situation.
How do you know what situation you are dealing with?
In the case where the given angle is acute, the height of the triangle should be calculated.

1. If the opposite side is less than the height [a <>
2. If the opposite side is equal to the height [a = h] OR the opposite side is greater than the adjacent side [a > b], then only one triangle is possible.
3. If the height is less than the opposite side, which is less than the adjacent side [h < a < b], then there are two triangles possible.
   

Algebra I: Lesson Plan * 9/28/2006

Quickstart
p.139 #81 - 91 odd

FCAT Pre-Test Discussion
#4 (A.2.4.2, A.3.4.2) and
#7 (B.1.4.1)

MA.B.1.4.1 Practice Problems
Worksheet

PreCalculus: Lesson Plan * 9/28/2006

Quickstart p.418 #60 - 93 x 3's

Turn in 5.4 Quiz

Lesson
Return & Discuss 5.3 Quiz - Solving Trig Equations

Using Graphing Calculators
I. Verifying Identities
- p.386 Study Tip
- Writing about Math
II. Solving Trig Equations
- Graphical Solution: p.396 Exploration #1
- Numerical Solution: Use the table feature (see Example 2 p.393 for a similar example)

Review Chapter 5
Chapter 5 Self-Test p.426

REMINDER
Chapter 5 Test Friday, September 29

Algebra I: Lesson Plan * 9/27/2006

Quickstart
p. 124 #1 - 4

Chapter 2 Test

(3-1) Inequalities and Their Graphs FCAT Practice
p.139 #74 - 79

PreCalculus: Lesson Plan * 9/27/2006

Quickstart: Review for Chapter 4 ReTest

Chapter 4 ReTest
Lesson
(5.5) Multiple-Angle and Product-Sum Formulas [continued]
III. Half-Angle Formulas [continued]

IV Product-Sum Formulas
A. Product-to-sum formulas


B. Sum-to-product Formulas



2x = π/2, 3π/2, 5π/2, 7π/2 2x is double x so the interval is doubled [0, 4π)
x = π/4, 3π/4, 5π/4, 7π/4

cosx = 0
x = &pi;/2, 3π/2

5.4 Quiz
1. Find all solutions on the inverval [0, 2π):
= 1
2. Use the sum and difference formulas to write the expression as the sine, cosine, or tangent of an angle.
sin110°cos80° + cos110°sin80°

3. Find the exact value of sin 225°. (Use the fact that 225° = 210° + 45°.)

PreCalculus: Lesson Plan * 9/26/2006

• Quickstart
  p.410 #91, 93
  p.420 #111, 113, 115
• 5.4 Guided Practice
  Examples 1, 2, 4 from 5.4 Student Success Organizer
• Lesson
  5.5 Multiple-Angle and Product-Sum Formulas
  Objective: Students will know how to use multiple-angle formulas, power-reducing formulas and half-angle formulas to rewrite and evaluate trigonometric functions.
  
  I. Double-angle formulas
  
  
  
  
  II. Power-reducing formulas
  
  
  
  III. Half-angle formulas
  
  
  
  
• Homework p.418 #1 - 8, 17 - 58 x 3's, 103, 104, 105, 106
  

Algebra I: Lesson Plan * 9/25/2006

• Quickstart Checkpoint Quiz p.115 #1-10
  Check answers in the back of the book
• Lesson 2-4 thru 2-6 Quiz (10 points)
• Lesson
  2-7: Using Measures of Central Tendency
  mean, median, mode, range
  p.123 #31
  
• Homework
  p.121 - 122 # 1 - 18 x's, 24, 27
  

PreCalculus: Lesson Plan * 9/25/2006

• Quickstart Lesson 5.3 ACE Self-Test
  Please e-mail to instructor colleen.lynch@browardschools.com
  As text. Include your name.
• 5.3 Quiz
• Lesson
  5.4 Sum and Difference Formulas
  Objective: Know how to use sum and difference formulas to rewrite and evaluate trigonometric functions.
  
  1. Story of Sinbad and Cosette
  2. Definition of Sum and Difference Formulas
     
  3. Using Sum and Difference Formulas to find exact values of trigonometric functions for angles other than 30°, 45°, and 60° angles
     
  4. Using Sum and Difference Formulas to simplify trigonometric expressions
     Reduction Formulas
     
  5. Using Sum and Difference Formulas to solve trigonometric equations
     
     

• Homework p. 408 - 410 3 3 - 27 x 3's, 57, 60