EngageNY
Graphing the Sine and Cosine Functions
Doing is more effective than watching. Learners use spaghetti to discover the relationship between the unit circle and the graph of the sine and cosine functions. As they measure lengths on the unit circle and transfer them to a...
EngageNY
Transforming the Graph of the Sine Function
Build a solid understanding of trigonometric transformations through exploration. Learners work in teams to analyze the effects of different algebraic components on the graph of a sine function.
CK-12 Foundation
Changes in Period and Amplitude of the Sine Function
How does a change in amplitude or period affect the equation of a sine function? Scholars move sliders to change the frequency and period of the sine function. The interactive displays the resulting equation, and pupils determine the...
CK-12 Foundation
Horizontal Translations or Phase Shifts: Sine
Shift a trigonometric function and find its new equation. Pupils translate a sine function on a graph. The scholars determine the equation of the function that represents the translated graph and observe the connection between a...
EngageNY
The Height and Co-Height Functions of a Ferris Wheel
Show learners the power of mathematics as they model real-life designs. Pupils graph a periodic function by comparing the degree of rotation to the height of a ferris wheel.
CK-12 Foundation
Translating Sine and Cosine Functions: Translating Sine
Learn how to slide sine back and forth and up and down. Pupils move the starting point of a graph of sine vertically and horizontally. They investigate the changes to the equation of the graph in relationship to the translation. They...
CK-12 Foundation
Sine Graph and Cosine Graph: Changing Amplitude
Scholars manipulate the amplitude of the graphs of sine and cosine, notice how the change in amplitude is reflected in their graphs, and answer several questions about the concept they noticed.
Mt. San Antonio Collage
Graphing Trigonometric Functions
Double win with a comprehensive worksheet and an excellent worked out answer key. The worksheet itself is twelve pages and begins with the simple sine and cosine graphs, then, develops into the reciprocal trig functions.
EngageNY
Revisiting the Graphs of the Trigonometric Functions
Use the graphs of the trigonometric functions to set the stage to inverse functions. The lesson reviews the graphs of the basic trigonometric functions and their transformations. Pupils use their knowledge of graphing functions to model...
EngageNY
Transformations of the Graphs of Logarithmic and Exponential Functions
Transform your lesson on transformations. Scholars investigate transformations, with particular emphasis on translations and dilations of the graphs of logarithmic and exponential functions. As part of this investigation, they examine...
EngageNY
Properties of Trigonometric Functions
Given a value of one trigonometric function, it is easy to determine others. Learners use the periodicity of trigonometric functions to develop properties. After studying the graphs of sine, cosine, and tangent, the lesson connects them...
Concord Consortium
Adding the Sines
It's a sign! Scholars analyze sine functions for patterns in their periods. The exploration advances beyond a simple function to the combination of two functions with even and odd coefficients. Their goal is to find a pattern between the...
Project Maths
Trigonometric Functions
From a circle to a cycle! The final lesson of a five-part series challenges learners to use points from the unit circle to plot a repeating pattern. The repeating patterns become the graphs of the trigonometric functions. Scholars also...
West Contra Costa Unified School District
Introduction to Trigonometric Functions
Scholars first learn the definitions of the sine ratio, the cosine ratio, and the tangent ratio. After mastering these definitions, they use the new information to solve triangles.
CK-12 Foundation
Derivatives of Trigonometric Functions: Derivative of sin(x)
Graphically find the derivative of sin(x). Using the interactive, pupils graph the slope of the tangent line to the sine function. Class members use the resulting graph to determine the derivative of the sine function. They verify their...
Alabama Learning Exchange
Technology for Displaying Trigonometric Graph Behavior: Sine and Cosine
Students explore the concept of sine and cosine. In this sine and cosine lesson, students work in groups to graph sine and cosine functions. Students examine how coefficients in various parts of each parent function shift the graph. ...
Coastal Carolina University
Graphs of the Six Trigonometric Functions
Your learners will appreciate having this color-coded set of the six trigonometric functions all on one page. Included are the graphs for sine, cosine, tangent, cosecant, secant, and cotangent. Notice that part of each graph is bolded to...
Mathematics Vision Project
Module 6: Trigonometric Functions
Create trigonometric functions from circles. The first lesson of the module begins by finding coordinates along a circular path created by a Ferris Wheel. As the lessons progress, pupils graph trigonometric functions and relate them to...
EngageNY
Awkward! Who Chose the Number 360, Anyway?
Don't give your classes the third degree. Use radians instead! While working with degrees, learners find that they are not efficient and explore radians as an alternative. They convert between the two measures and use radians with the...
EngageNY
Inverse Trigonometric Functions
Build on the understanding of finding angles using trigonometric ratios. Pupils develop the definitions of inverse trigonometric functions by restricting their domains in the 13th instructional activity of a 16-part series. They use...
Curated OER
Exercise Set 5.4: Inverse Trigonometric Functions
For this trigonometric functions worksheet, high schoolers solve 68 multi-part short answer and graphing questions. Students evaluate inverse trigonometric functions for a given value. High schoolers graph inverse trigonometric functions.
Flipped Math
Unit 10 Review: Graphing Sine and Cosine
Go up and down with a review. Learners review finding the amplitude, midline, period, and frequency of sinusoidal functions and use that information to draw graphs. Pupils arrive at equations for function from graphs. They finish up the...
CK-12 Foundation
Vertical Translations: Vertical Shift of Sinusoidal Functions
Create a shift in TV viewing habits. The interactive presents a cosine model of an individual's TV viewing habits during a year. Class members move the model to reflect given conditions. Finally, they determine key features from the...
Curated OER
Woody Sine
Students explore the concept of sine. For this sine lesson, students create a sine graph from tooth picks. Students create a unit circle with tooth pick length radius. Students then take the tooth picks from the unit circle and put them...