Trigonometric Functions

• Explanation:

  • Notes | Annotated

  • Khan video: Interpreting trigonometric graphs in context (5:33)

  • Khan video: Features of sinusoidal functions  (4:57)

  • Khan article: Midline, amplitude, and period review

  • Khan video: Periodicity of algebraic models (3:20)

  • video of the frequency of noise and water

  • video: Mathematics of Vibration

• Practice Problems:

  • Desmos: Function 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: Interpreting trigonometric graphs in context 

    • Khan Exercise: Periodicity of algebraic models (challenging)

    • IXL: Algebra 2: AA.1 Find properties of sine functions (stop at 64; after 64 it starts with equations); vertical shift is the same as the midline

    • IXL Algebra 2: AA.6 Find properties of cosine functions (stop at 64; after 64 it starts with equations); vertical shift is the same as the midline

    • Worksheet #1

• Explanation: 

  • Notes | Annotated

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

  • Khan video: Introduction to Radians (10:50)

  • Khan video: Radians & degrees (7:10)

  • Khan video: Degrees to radians (7:01)

  • Khan video: Radians to degrees (3:19)

  • Khan video: Radian angles & quadrants (honors) (3:50)

• Practice Problems:

  • Khan exercise: Radians & degrees

  • IXL: Algebra 2: Y.1 Convert between radians and degrees EDC

• • • Worksheet #1

Explanation:

• Review six ratios | Annotated

• Using trig ratios to find the missing sides or angles in a right triangle Notes | Annotated

Practice Problems:

• Review: Using trig ratios to find the missing sides or angles in a right triangle WS#1

• Khan Exercise: Solve for a side in right triangles

• Khan Exercise: Solve for an angle in right triangles

• Explanation:

  • Completed Unit Circle: pdf 

  • Notes | Annotated

  • Website: Math is Fun: Unit circle

  • Khan video: Unit circle (9:03)

  • Khan video: The trig functions & right triangle trig ratios (6:56)

  • Khan article: Trig unit circle review

  • Khan video: Trig values of special angles (7:53)

  • Desmos graph (shows the physical distances of all six trig ratios on the unit circle)

• Practice Problems:

  • Quizlet 

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

  • Khan Exercise: Unit circle only sine and cosine and only degrees; students must convert between reference angle the given angle)

  • Khan exercise: Unit circle (with radians) (only sine and cosine)

  • IXL: Algebra 2: Z.7 Sin, cos, and tan of special angles (score of 68 - after includes negative angles) - requires rationalizing the denominator

  • IXL: Algebra 2: Z.8 Csc, sec, and cot of special angles (score of 68)

  • Worksheet #1

  • Demsos Activity: Unit Circle (teacher use)

• Teacher resource:

  • Purchase Unit Circle pdfs 

• Explanation

  • Khan video: Proof of the Pythagorean trig identity (6:11)

  • Khan video: Using the Pythagorean trig identity (6:14)

  • Khan Article: Pythagorean identity Review 

• Practice Problems

  • Khan exercise: Use the Pythagorean identity 

• • 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; challenging)

    • IXL (Precalculus): M.9 Inverses of trigonometric functions (only if rationalization was taught)

    • IXL (Precalculus): M.11 Solve trigonometric equations 

    • Worksheet #1 

• Explanation:

  • Graphs from the Unit Circle Task String Directions 

  • Graphs from the unit Circle Task Ruler Directions (use this plane)

  • Sine Graph on desmos

  • Cosine Graph on desmos

  • Khan video: Graph of y=sin(x) (9:21)

  • Khan video: Intersection points of y=sin(x) and y=cos(x) (11:06)

• Practice Problems:

• • • Graphs from the Unit Circle WS

• Explanation:

  • Notes | Annotated

  • Khan video: Amplitude & period of sinusoidal functions from equation (8:20)

  • Khan video: Transforming sinusoidal graphs: vertical stretch & horizontal reflection (12:51)

• Practice Problems:

  • Khan Exercise: Amplitude of sinusoidal functions from equation

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

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

• • • Worksheet #1

• Explanation:

  • Notes | Annotated

  • Khan video: Transforming sinusoidal graphs: vertical & horizontal stretches (12:51)

  • Khan video: Example: Graphing y=3⋅sin(½⋅x)-2 (3:23)

  • Khan video: Example: Graphing y=-cos(π⋅x)+1.5 (3:10)

  • Khan video: Sinusoidal function from graph (5:21)

• Practice Problems:

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

    • Khan Exercise: Graph sinusoidal functions (challenging)

    • Khan Exercise: Construct sinusoidal functions  (honors)

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

    • IXL: Algebra 2: AA.1 Find properties of sine functions (stop at 75)

    • IXL: Algebra 2: AA.6 Find properties of cosine functions (stop at 75)

    • 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)

    • Worksheet #1

• • Explanation:

    • Notes | Annotated Notes

    • Khan video: Trig word problem: modeling daily temperature (10:54)

    • Khan video: Trig word problem: modeling annual temperature (6:45)

    • Khan video: Trig word problem: length of day (phase shift) (honors: 7:42)

  • Practice Problems:

    • Khan exercise: Modeling with sinusoidal functions (honors)

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

    • Worksheet #1 

• Explanation:

  • Notes | Annotated

  • Khan video: Graph of y=tan(x) (10:11)

  • Website: animated graph of y = tanx

• Practice Problems:

  • Worksheet #1

• Summary Notes

• Concept Review WS

• Worksheet #1

• Worksheet #2

Cumulative Review #3 WS