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### Unit Circle & Graphing

 Essential Question: How can we model periodic (repeating) and fluctuating (oscillating) data?  Angles 1)  Degree and Radian Measurements and Conversion Explanation: Notes | AnnotatedVideos:Khan: Introduction to RadiansKhan: Radians & degreesKhan: Degrees to radiansKhan: Radians to degreesKhan: Radian and degree conversion practiceWebsite that animates the number of radians in a circleExplanation and extra examples from purplemath (at the bottom of the page) Practice Problems:Worksheet #1 | AnswersWorksheet #2Khan Exercise: Degrees to Radians 2)  Coterminal and Reference Angles   Explanation: Practice Problems: Trig Operations 3)  Trig on a Coordinate Plane Explanation Notes | Annotated 4) Completing the Unit Circle:  Explanation: Completed Unit Circle:  Khan video: Introduction to the unit circleKhan article: Trig unit circle review Practice: 5)  Exact Trig Ratios on a Unit Circle:  Explanation: Notes | Annotated NotesKhan video: Unit circleKhan article: Trig unit circle reviewKhan video: Trig values of special anglesDesmos graph (physical distances of all six trig ratios) Practice Problems: QuizletKhan Exercise: Trig values of special angles (only sine and cosine) Worksheet #1  Worksheet #2  Worksheet #3 6)  Inverse Trig Ratios on a Unit Circle: Explanation: Notes | Annotated Notes Practice Problems: 7)  Order of Operations with Trig Ratios:  Explanation: Notes | Annotated Notes Practice Problems: Graphing Trig Functions     8)  Graphing Sin and Cosine from the Unit Circle:   Explanation:Khan Video: Graph of y=sin(x)Khan video: Intersection points of y=sin(x) and y=cos(x)Interactive graphs of the relationship between the unit circle and the graph of sin and cos curve:Sine Graph on desmosCosine Graph on desmoswebsite (quicktime)Tacoma Bridge collapses Large Coordinate Plane handoutModified directions from Illuminations: Graphs from the Unit Circle Practice Problems:Graphs from the Unit Circle WS 9)  Transformations of sin and cos: Amplitude and Period  Explanation: Desmos Activity: Polygraph: Sinusoids with Vertical Transformations (teacher use only)Blank Trig Coordinate Planes Notes | AnnotatedKhan video: Transforming sinusoidal graphs: vertical & horizontal stretches Interactive Websites: Graph sin with change in amplitude with Desmos Graph cos with change in amplitude with Desmos Graph sin with change in period (multiplying by a number) with Desmos Graph sin with change in period (dividing by a number) with Desmos Graph cos with change in period (multiplying by a number) with Desmos Graph cos with change in Period (dividing by a number) with Desmos NLVM (Interactive website using java by the Utah State University - NLVM): graph any trig function; also make your own graph with up to three sliding variablesvideo of frequency of noise and water Practice Problems: 10) Transformation of sin and cos: Vertical Shift (shift the x-axis or "midline") Explanation Notes | Annotated Practice Problems: Khan Exercise: Graph sinusoidal functions (challenging)Worksheet #1 Worksheet #2 Worksheet #3 11)  Transformation of sin and cos: Horizontal Shift (shift the y-axis or Phase Shift) Explanation: Practice Problems Worksheet #1  Worksheet #2 Worksheet #3Khan Exercise: Graph sinusoidal functions: phase shift (challenging)  12)  Identify Parts of a Trig Function from an Equation (and Graphing Mixed Review) Explanation:  Identify Parts of a Trig Function: Notes | AnnotatedGraphing Mixed Review: Notes | AnnotatedSound Waves Practice Problems: Desmos Polygraph: Sinusoids (Teacher Use Only)Khan exercise: Midline of sinusoidal functions from equationKhan exercise: Amplitude of sinusoidal functions from equationKhan exercise: Period of sinusoidal functions from equation (give answers in terms of radians) Identify Parts of a Trig Function WS #2Graphing Sin and Cosine by Transformations (Mixed Review): 13) Writing Sine and Cosine Functions Explanation vocabulary review Khan article: Midline, amplitude, and period reviewKhan Video:  Features of sinusoidal functionsKhan Video: Sinusoidal function from graph Khan video: Predator-prey cycles Practice Problems: Desmos Activity: Trigonometric Graphing: Introduction to Amplitude and Vertical Shift (Teacher use only)Desmos Activity: Graphing the Sine Function using Amplitude, Period, and Vertical Translation (Teacher use only)Desmos Activity: Marbleslides (Teacher use only)Desmos Activity: Burning Daylight (Teacher use only)Worksheet #1Worksheet #2 Khan Exercise: Midline of sinusoidal functions from graphKhan Exercise: Amplitude of sinusoidal functions from graphKhan Exercise: Period of sinusoidal functions from graphKhan Exercise: Construct sinusoidal functionsKhan Exercise: Modeling with sinusoidal functionsKhan Exercise: Modeling with sinusoidal functions: phase shift Math Modeling with Trig Project  Foxes and Rabbits 14)  Graphing Secant & Cosecant Functions Explanation: Practice Problems: 15) Graphing Tangent & Cotangent Functions Explanation Notes | Annotated Kahn Video: Graph of y=tan(x) Desmos: example of transforming tangentDesmos: example of transforming cotangent Practice Problems: 16)  Unit Circle and Graphing Trig Functions Review  17)  Unit Circle Cumulative Review WS Common Core Standard: Functions: Trigonometric FunctionsExtend the domain of trigonometric functions using the unit circle:A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.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 x, π + x, and 2π - x in terms of their values for x, where x is any real number.Model periodic phenomena with trigonometric functions:B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Resources: http://www.intmath.com/trigonometric-graphs/trigo-graph-intro.php