| Unit 3: Trigonometric Functions |
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Activity 14
Angles and Angle Measure
14-1 Learning Targets:
- Draw angles in standard position.
- Find the initial side and terminal side of an angle in standard position.
- Identify coterminal angles.
14-2 Learning Targets:
- Measure angles in radians.
- Convert angle measures from degrees to radians.
- Recognize trigonometric ratios to complete reference triangles.
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Radian Measure |
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Introduction to radians
Rotation by radians and quadrants
Finding arc length from radian angle measure
Example: Radian measure and arc length
Example: Converting degrees to radians
Example: Converting radians to degrees
Radian and degree conversion practice
Radians and degrees
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Activity 15
Sinusoidal Functions
15-1 Learning Targets:
- Recognize situations that involve periodic data.
- Sketch a graph of periodic data.
15-2 Learning Targets:
- Explore how a change in parameters affects a graph.
- Determine the period, amplitude, or phase shift of a periodic function.
15-3 Learning Targets:
- Graph a periodic function with various domains.
- Compare the graph of y = sin x to periodic graphs.
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Exploring Periodic Data |
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Modeling annual temperature variation with trigonometry
Modeling temperature through the day
Day length in Alaska
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| Periodic Functions |
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Midline, amplitude and period of a function
Example: Amplitude and period
Example: Amplitude and period transformations
Example: Amplitude and period cosine transformations
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| Graph of the Sine and Cosine Function |
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Example: Graph, domain, and range of sine function
Example: Graph of cosine
Example: Intersection of sine and cosine
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Activity 16
Trigonometric Functions and the Unit Circle
16-1 Learning Targets:
- Label points on the unit circle.
- Use the unit circle to find trigonometric values.
16-2 Learning Targets:
- Define the reciprocal trigonometric functions using the unit circle.
- Evaluate all six trigonometric functions for an angle in standard position
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The Unit Circle |
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Introduction to the unit circle
Unit circle manipulative
Matching ratios to trig functions
Solving triangle in unit circle
Finding trig functions of special angles example
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| Reciprocal Trigonometric Functions |
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Secant (sec), cosecant (csc) and cotangent (cot) example
Example: Using trig to solve for missing information
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Activity 17
Graphs of the form y = A sin[B(x – C)] + D
17-1 Learning Targets:
- Graph a trigonometric function over a specified interval.
- Describe how changing parameters affect a trigonometric graph..
17-2 Learning Targets:
- Find the amplitude and period of a trigonometric function.
- Write a trigonometric function given its graph.
- Model situations with trigonometric functions.
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Trigonometric Graphs |
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Example: Figure out the trig function
Determining the equation of a trig function
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Activity 18
Graphs of Trigonometric Functions
18-1 Learning Targets:
- Sketch the graphs of csc x, sec x, tan x, and cot x.
- Find the period and locate asymptotes of reciprocal trig functions.
- Determine the domain and range of reciprocal trig functions.
18-2 Learning Targets:
- Graph transformations of reciprocal trig functions.
Describe how changing parameters affect a trigonometric graph.
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Activity 19
Inverse Trigonometric Functions
19-1 Learning Targets:
- Apply a trigonometric function to a real-world situation.
- Define and apply the inverse cosine function.
19-2 Learning Targets:
- Relate one-to-one functions to inverse trigonometric functions.
- Define and apply the inverse sine function.
19-3 Learning Targets:
- Define and apply the inverse tangent function.
Find values of inverse trigonometric functions.
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Inverse Cosine Functions |
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Inverse trig functions: arccos
Example: Calculator to evaluate inverse trig function
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| Inverse Sine Functions |
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Inverse trig functions: arcsin
Example: Calculator to evaluate inverse trig function
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| Inverse Tangent Functions |
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Inverse trig functions: arctan
Example: Calculator to evaluate inverse trig function
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| Modeling with Trigonometric Functions |
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Inverse tan domain and range
Inverse tangent scenario
Angle of sun with the ground based on shadow
Modeling annual temperature variation with trigonometry
Applying inverse trig function with model
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Activity 20
Solving Simple Trigonometric Equations
20-1 Learning Targets:
· Apply a trigonometric equation to represent a real-world situation.
· Find the general solution to a trigonometric equation
20-2 Learning Targets:
· Use reference angles to solve trigonometric equations.
· Find the solution to a trigonometric equation over an interval.
Generate a trigonometric equation for a real-world situation
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