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Mr. Wolf
Monday 12/8/08
Geometry
Grades 10-12
Unit 7: Right Triangles
Inverse Trig Functions & Real World Applications
Materials and Resources:
 Warm-up (1 per student)
 Inverse Trigonometric Functions sheet (1 per student)
 Exit Ticket (1 per student)
PA Standards Addressed:
Instructional Objectives:
 Students will be able to evaluate inverse trigonometric functions.
 Students will be able to solve for missing angles in right triangles.
 Students will be able to solve real world applications of right triangle
trigonometry.
Time
10 min
1 min
40 min
Activity
Warm-up
Agenda
Inverse Trig
Functions
Pg. 308 #11-12
Pg. 314 #1, 2, 6
35 min
Real World
Applications
Pg. 319 #4, 5
1 min
5 min
Agenda
Conclusion
Homework:
Pg. 308 #5-9
Pg. 314 #3-5, 7, 8
Pg. 319 #3, 6
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.
Geometry Fall 2008
Name: ________________________
Warm-up
Use a calculator to find the value of the following trigonometric functions. Round
answers to the nearest hundredth.
sin(24°) =
cos(55°) =
tan(80°) =
Use a calculator to find the value of x. Round answers to the nearest hundredth.
cos(35°) =
x
7
x = ________
tan(12°) =
4
x
sin(68°) =
x = ________
x
8
x = ________
Find the values of x in the following triangles.
Geometry Fall 2008
Name: ________________________
Warm-up
Use a calculator to find the value of the following trigonometric functions. Round
answers to the nearest hundredth.
sin(24°) =
cos(55°) =
tan(80°) =
Use a calculator to find the value of x. Round answers to the nearest hundredth.
cos(35°) =
x
7
x = ________
tan(12°) =
4
x
x = ________
Find the values of x in the following triangles.
sin(68°) =
x
8
x = ________
Geometry Fall 2008
Name: ________________________
Inverse Trigonometric Functions
Recall that sin(x), cos(x), and tan(x) are all functions of x. Therefore, we want to
examine the inverse functions.
Trigonometric Functions
Basic Operations
Function
Inverse Function
Operation
Inverse Operation
Sine
Inverse Sine
Addition
Subtraction
sin(x)
sin-1(x)
+
–
Cosine
Inverse Cosine
Multiplication
Division
cos(x)
cos-1(x)
•
÷
Tangent
Inverse Tangent
tan(x)
tan-1(x)
To evaluate the inverse sine, cosine, or tangent with a graphing calculator:
1) Hit the
key in order to activate the secondary commands
2) Hit the
,
, or
wish to evaluate
3) Enter the angle measure
4) Hit
key depending on which inverse function you
Examples: Evaluate the following trigonometric inverse functions. Round answers to the
nearest whole number.
sin-1(0.4068) =
cos-1(0.5736) =
tan-1(5.6713) =
Examples: Solve the following equations for x. Round answers to the nearest whole
number.
sin(x) = 0.9063
x = ______
cos(x) = 0.9397
tan(x) = 1
x = ______
x = ______
Finding Unknown Angle Measures
To find an unknown angle measure…
1) Set up a sine, cosine, or tangent proportion
2) Use the inverse sin, cos, tan button on your calculator and solve for the
missing value.
Example: Solve for x.
Geometry Fall 2008
Name: ________________________
Real World Applications
Suppose an operator at the top of a lighthouse sights a sailboat on a line that makes a 25º
angle with a horizontal line. The angle between the horizontal and the line of sight is
called an angle of depression. At the same time, a person in the boat must look 25º
above the horizontal to see the tip of the lighthouse. This is called an angle of elevation.
If the top of the lighthouse is 40m above sea level, the distance x between the boat and
the base of the lighthouse can be calculated.
Example:
A sled travels from point A at the top of the hill to point B at the bottom. The angle of
depression of the hill (or the steepness) is 35º. If the elevation of point A is 75 yards, find
the distance the sled travels.
(Hint: Draw a diagram first!)
Geometry Fall 2008
Name: ________________________
Exit Ticket
Bjorn Snurgensen, the most famous Swedish Olympic athlete, one a gold medal at the
1964 Olympics by throwing a javelin 84 meters. At the halfway point of its journey, the
javelin reached its maximum height of 25 meters. Calculate the angle of elevation that
Bjorn threw the javelin.
1) Draw a figure to represent the above scenario.
2) Label the distance traveled, the halfway point, and the maximum height of the
javelin
3) Label the angle of elevation as x
4) Set up a trigonometric ratio and solve for x
Geometry Fall 2008
Name: ________________________
Exit Ticket
Bjorn Snurgensen, the most famous Swedish Olympic athlete, one a gold medal at the
1964 Olympics by throwing a javelin 84 meters. At the halfway point of its journey, the
javelin reached its maximum height of 25 meters. Calculate the angle of elevation that
Bjorn threw the javelin.
1) Draw a figure to represent the above scenario.
2) Label the distance traveled, the halfway point, and the maximum height of the
javelin
3) Label the angle of elevation as x
4) Set up a trigonometric ratio and solve for x