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Mr. Wolf
Pre-Calculus
Monday 12/22/08
Grades 11-12
Unit 5: Graphs & Inverses of Trigonometric Functions
Review Unit 5
Materials and Resources:
 Warm-up (1 per student)
 Unit 5 Study Guide (1 per student)
 Exit ticket (1 per student)
PA Standards Addressed:
Instructional Objectives:
 Students will be able to solve real world applications of trigonometric functions.
 Students will be able to review for the Unit 5 Test.
Time
10 min
1 min
45 min
Activity
Warm-up
Agenda
Real World
Applications
35 min
Unit 5 Review
1 min
5 min
Agenda
Conclusion
Homework:
Study for Unit 5 Test
Lesson Reflection:
Description
Pass out the warm-up and review solutions.
Review the goals for the day.
Modeling:
Guiding:
Independent Practice:
Assessment:
Modifications:
Students with special needs…
Advanced students…
Modeling:
Guiding:
Independent Practice:
Assessment:
Modifications:
Students with special needs…
Advanced students…
Revisit goals and identify whether they were met.
Pass out the Exit Ticket and collect at the bell.
Pre-Calculus Fall 2008
Name: ________________________
Warm-up
A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is
slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep
end. Find the angle of depression of the bottom of the pool.
Pre-Calculus Fall 2008
Name: ________________________
Warm-up
A swimming pool is 20 meters long and 12 meters wide. The bottom of the pool is
slanted so that the water depth is 1.3 meters at the shallow end and 4 meters at the deep
end. Find the angle of depression of the bottom of the pool.
Pre-Calculus Fall 2008
Name: ________________________
Unit 5 Study Guide
Section 4.5 Graphs of Sine and Cosine Functions
 Sketch graphs of y  sin x and y  cos x
 Describe the effects of a, b, c, and d values on the shifts and transformations of
y  d  a sin( bx  c) and y  d  a cos(bx  c)
 Identify domain, range, amplitude, period, maximum, minimum, x-intercepts, yintercepts of sine and cosine curves
 Sketch graphs of sine and cosine curves
 Write the equations of sine and cosine graphs
Section 4.6 Graphs of Other Trigonometric Functions
 Sketch graphs of y  sec x , y  csc x , y  tan x , and y  cot x
 Describe the effects of a, b, c, and d values on the shifts and transformations of
y  d  a sec(bx  c) , y  d  a csc(bx  c) , y  tan( bx  c) , and y  cot( bx  c)
 Identify domain, range, amplitude, period, asymptotes, maximum, minimum, xintercepts, y-intercepts of secant, cosecant, tangent, and cotangent curves
 Sketch graphs of secant, cosecant, tangent, and cotangent curves
 Write the equations of secant, cosecant, tangent, and cotangent graphs
Section 4.7 Inverse Trigonometric Functions
 Define the domain and range of the inverse trigonometric functions
 Evaluate arcsin, arcos, and arctan functions
 Evaluate compositions of inverse trigonometric functions with basic trigonometric
functions at standard angles (0, 30º, 60º, 90º, etc.)
 Evaluate compositions of inverse trigonometric functions with basic trigonometric
functions at non-standard angles by sketching a right triangle
Section 4.8 Applications and Models
 Solve a right triangle by applying SOHCAHTOA ratios and the Pythagorean
Theorem to find all side lengths and angle measurements
 Apply solving a right triangle in real world situations
 Apply solving a right triangle to determine directional bearings
 Identify amplitude, frequency, and period in order to write the equations of simple
harmonic motion
 Solve simple harmonic motion problems
Pre-Calculus Fall 2008
Name: ________________________
Exit Ticket
Identify the topics you will focus your studying on tonight:
 Sketching graphs of trigonometric functions
 Describing the effects of a, b, c, and d values on the shifts and transformations
 Identifying domain, range, amplitude, period, maximum, minimum, x-intercepts,
y-intercepts of trigonometric function graphs
 Writing the equations of trigonometric function graphs
 Defining the domain and range of the inverse trigonometric functions
 Evaluating arcsin, arcos, and arctan functions
 Evaluating compositions of inverse trigonometric functions with basic
trigonometric functions at standard angles (0, 30º, 60º, 90º, etc.)
 Evaluate compositions of inverse trigonometric functions with basic trigonometric
functions at non-standard angles by sketching a right triangle
 Apply solving a right triangle in real world situations
 Identify amplitude, frequency, and period in order to write the equations of simple
harmonic motion
 Solve simple harmonic motion problems
Pre-Calculus Fall 2008
Name: ________________________
Exit Ticket
Identify the topics you will focus your studying on tonight:
 Sketching graphs of trigonometric functions
 Describing the effects of a, b, c, and d values on the shifts and transformations
 Identifying domain, range, amplitude, period, maximum, minimum, x-intercepts,
y-intercepts of trigonometric function graphs
 Writing the equations of trigonometric function graphs
 Defining the domain and range of the inverse trigonometric functions
 Evaluating arcsin, arcos, and arctan functions
 Evaluating compositions of inverse trigonometric functions with basic
trigonometric functions at standard angles (0, 30º, 60º, 90º, etc.)
 Evaluate compositions of inverse trigonometric functions with basic trigonometric
functions at non-standard angles by sketching a right triangle
 Apply solving a right triangle in real world situations
 Identify amplitude, frequency, and period in order to write the equations of simple
harmonic motion
 Solve simple harmonic motion problems