Trigonometric Functions

5.1 Periodic Functions: determine basic characteristics of sinusoidal functions (midline, amplitude, and period) given a graph

• Explanation:

  • Notes | Annotated

  • Khan Video: Features of sinusoidal functions

  • Khan Article: Midline, amplitude, and period review

  • Khan video: Periodicity of algebraic models

  • video of the frequency of noise and water

• Practice Problems:

  • Desmos Activity: Functions Carnival (teacher use only; skip to the Ferris Wheel problem).

• • • More Ferris Wheel Problems with Geobra

    • Khan Exercise: Midline of sinusoidal functions from graph

    • Khan Exercise: Amplitude of sinusoidal functions from graph

    • Khan Exercise: Period of sinusoidal functions from graph (challenge: uses radians and uses points that are 1 revolution, 1/2 of a revolution, or 1/4 of a revolution)

    • Khan Exercise: Periodicity of algebraic models

    • Worksheet #1

5.2 Convert Angle Measures between Degrees and Radians

• Explanation:

  • Notes | Annotated

  • Animation of the radius wrapped around a circle: Wikipedia | Math is Fun

  • Khan video: Introduction to Radians

  • Khan video: Radians & degrees

  • Khan video: Degrees to radians

  • Khan video: Radians to degrees

• Practice Problems:

  • Khan Exercise: Radians & degrees

• • • Worksheet #1

5.3 Trig Ratios on a Unit Circle

• Explanation:

  • Review six ratios

  • Completed Unit Circle: pdf | Notes

  • Khan video: Unit circle

  • Khan video: The trig functions & right triangle trig ratios

  • Khan article: Trig unit circle review

  • Khan video: Trig values of special angles

  • Desmos graph (physical distances of all six trig ratios)

• Practice Problems:

  • Quizlet

  • Khan Exercise: Trig values of special angles (only sine and cosine)

  • Khan Exercise: Unit circle

  • Khan exercise: Unit circle (with radians)

  • Worksheet #1

• Teacher resource:

  • Purchase pdfs

5.4 Graphs of Sine and Cosine Functions

• Explanation:

  • Graphs from the Unit Circle Task Directions (or use this plane)

  • Sine Graph on desmos

  • Cosine Graph on desmos

  • Khan video: Graph of y=sin(x)

  • Khan video: Intersection points of y=sin(x) and y=cos(x)

• Practice Problems:

• • • Graphs from the Unit Circle WS

5.5 Stretching and Compressing Sine and Cosine Functions: amplitude and period change

• Explanation:

  • Notes | Annotated

  • Khan video: Amplitude & period of sinusoidal functions from equation

  • Khan video: Transforming sinusoidal graphs: vertical & horizontal stretches

• Practice Problems:

  • Khan Exercise: Amplitude of sinusoidal functions from equation

  • Desmos Activity: Stretching and Compressing Sine and Cosine Functions (teacher use only)

  • Khan Exercise: Period of sinusoidal functions from equation (answers are in radians)

• • • Worksheet #1

5.6 Shifts of Sine and Cosine Functions: midline and phase shift change

• Explanation:

  • Notes | Annotated

  • Khan video: Sinusoidal function from graph

• Practice Problems:

• • • Khan Exercise: Midline of sinusoidal functions from equation

    • Desmos Activity: Transformation of Sine and Cosine Functions (teacher use)

    • Desmos Activity: Trigonometric Graphing: Introduction to Amplitude and Vertical Shift (Teacher use)

    • Desmos Activity: Graphing the Sine Function using Amplitude, Period, and Vertical Translation (teacher use ; the period is challenging)

    • Desmos Activity: Marbleslides: Periodics (teacher use)

    • Khan Exercise: Graph sinusoidal functions (challenging)

    • Khan Exercise: Construct sinusoidal functions (challenging)

    • Khan Exercise: Graph sinusoidal functions: phase shift (challenging)

    • Worksheet #1

5.7 Modeling with sinusoidal functions

• • Explanation:

    • Notes | Annotated Notes

    • Khan video: Trig word problem: modeling daily temperature

    • Khan video: Trig word problem: modeling annual temperature

    • Khan video: Trig word problem: length of day (phase shift) (extra)

  • Practice Problems:

    • Khan exercise: Modeling with sinusoidal functions

    • Khan exercise: Modeling with sinusoidal functions: phase shift (extra credit)

    • Worksheet #1

5.8 Graph Tangent and Cotangent Functions

• Explanation:

  • Notes | Annotated

  • Khan video: Graph of y=tan(x)

  • Website: animated graph of y = tanx

• Practice Problems:

  • Worksheet #1

5.9 Inverse Trig Ratios

• • Explanation:

    • Notes | Annotated Notes

    • Khan article: Inverse trigonometric functions review

    • Khan video: Intro to arcsine

    • Khan video: Intro to arctangent

    • Khan video: Intro to arccosine

  • Practice Problems:

    • Khan exercise: Evaluate inverse trig functions (with a calculator)

    • Worksheet #1

    • Worksheet #2

    • Worksheet #3

Review

• Summary Notes

• Concept Review WS

• Worksheet #1

• Worksheet #2

Cumulative Review #3 WS