Unit Circle and Trigonometric Functions

Lesson 14

Objective

Model contextual situations using trigonometric functions (Part II).

Common Core Standards

Core Standards

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  • F.TF.A.3 — Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π-x in terms of their values for x, where x is any real number.

  • F.TF.B.5 — Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Modeling is best interpreted not as a collection of isolated topics but in relation to other standards. Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.

Criteria for Success

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  1. Describe the meaning of parameters for sine and cosine functions in context. 
  2. Verify and describe the model in the context of the situation. 
  3. Define alternative models that may be used for a contextual situation. 

Anchor Problems

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Problem 1

Have students participate in the Desmos activity Burning Daylight.

Guiding Questions

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References

Desmos Burning Daylight

Burning Daylight by is made available by Desmos. Copyright © 2017 Desmos, Inc. Accessed Feb. 26, 2018, 4:58 p.m..

Problem 2

Have students participate in the activity Moon Safari by Kate Nowak on her blog f(t).

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

f(t) Moon Safari

Moon Safari by Kate Nowak is made available on Function of Time under the CC BY-NC-SA 3.0 license. Accessed Feb. 27, 2018, 4 p.m..

Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

Target Task

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Tidal data for New Canal Station, located on the shore of Lake Pontchartrain, LA and Lake Charles, LA are shown below.

New Canal Station on Lake Pontchartrain, LA, Tide Chart

Date Day Time Height High/Low
2014/05/28 Wed. 07:22 a.m. 0.12 L
2014/05/28 Wed. 07:11 p.m. 0.53 H
2014/05/29 Thurs. 07:51 a.m. 0.11 L
2014/05/29 Thurs. 07:58 p.m. 0.53 H

 

Lake Charles, LA, Tide Chart

Date Day Time Height High/Low
2014/05/28 Wed. 02:20 a.m. -0.05 L
2014/05/28 Wed. 10:00 a.m. 1.30 H
2014/05/28 Wed. 03:36 p.m. 0.98 L
2014/05/28 Wed. 07:05 p.m. 1.11 H
2014/05/29 Thurs. 02:53 a.m. -0.06 L
2014/05/29 Thurs. 10:44 a.m. 1.31 H
2014/05/29 Thurs. 04:23 p.m. 1.00 L
2014/05/29 Thurs. 07:37 p.m. 1.10 H

a. Would a sinusoidal fucntion of the form $${f(x)=A\mathrm{sin}(\omega (x-h))+k}$$ be appropriate to model the given data for each location? Explain your reasoning.

b. Write a sinusoidal function to model the data for New Canal Station.

References