Trigonometric Functions
Trigonometric functions can be used to model periodic functions.
5.1 Periodic Functions: determine basic characteristics of sinusoidal functions (midline, amplitude, and period) given a graph
Explanation:
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
Practice Problems:
Desmos: Function Carnival (teacher use only; skip to the Ferris Wheel problem).
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
5.2 Convert Angle Measures between Degrees and Radians
Explanation:
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
5.3 Trig Ratios on a Unit Circle
Explanation:
Completed Unit Circle: pdf
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:
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)
Demsos Activity: Unit Circle (teacher use)
Teacher resource:
5.4 Pythagorean Identity (honors)
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
5.5 Inverse Trig Ratios
Explanation:
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
5.6 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) (9:21)
Khan video: Intersection points of y=sin(x) and y=cos(x) (11:06)
Practice Problems:
5.7 Stretching and Compressing Sine and Cosine Functions: amplitude and period change
Explanation:
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)
5.8 Shifts of Sine and Cosine Functions: midline and phase shift change
Explanation:
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)
5.9 Modeling with sinusoidal functions
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
5.10 Tangent and Cotangent Functions
Explanation:
Khan video: Graph of y=tan(x) (10:11)
Website: animated graph of y = tanx
Practice Problems:
Review
Cumulative Review #3 WS