Graphing Trigonometric Functions Teacher Resources

Stretch out the curve to expand mathematical knowledge. Pupils learn the definition of period and find out how to determine it both from the graph and the equation of the function. Learners use the new skill in graphing periodic...

Roll through two graphs. Learners see how the points from the unit circle allow easy construction of the graphs for sine and cosine using an instructional video. They discover how to find the amplitude and midline both from the graphs...

Take a ride on a Ferris wheel. Using sliders to adjust the parameters of a Ferris wheel, pupils investigate the height of a point over time. The interactive traces out the curve on a time-height graph. Learners use what they learned to...

Time for classes to show what they've learned. Use several tasks to assess understanding of the trigonometric functions, unit circle, radians, and basic trigonometric identities.

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...

Work in reverse with the product becoming the given. Using a spreadsheet image of the graph of a trigonometric function, young scholars investigate methods of creating spreadsheet data that results in the given graph. The catch? The data...

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...

The midline of the mathematical model of the number of hours of sunlight is not 12 hours. Pupils use the modeling cycle to determine a function that will model the number of hours of sunlight at a location of their choosing. Using...

If cosine is shifted, how is its equation affected? Learners manipulate the graph of cosine by moving the y-intercept to different locations on the coordinate plane. Pupils determine the new equation that models the shifts.

Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of the...

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...

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...

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.

Fly through graphing functions with the Function Flyer. Young mathematicians use an interactive to graph different types of functions. A set of exploration questions has users investigate patterns in functions.

They say a graph is worth a thousand points. The interactive allows users to graph a wide variety of functions and equations. Using the included keyboard or typing directly into the list, learners determine the graph of a function....

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...

Predict an equation that waves up and down. Pupils set the height, radius, and period of a Ferris wheel. The learners write a sine equation to match the graph of the height of a point on the wheel as a function of time. Running the...

Find out what causes a function to slide. Pupils move a function along the x-axis and see the resulting change in its equation. Scholars determine the effects that the translation has on the intercepts, domain, and range of the function.

The inflection point, the point where the second derivative is zero, is the focus of a video  that works through a problem where it is not obvious to see the roots of a function. The solution to the problem requires using Newton's method...

Change the y-intercept by adding a constant to the function. Individuals move three functions vertically along the y-axis. As they observe how the equation of the functions change with the vertical movement, learners determine how to...

Find the volume of a rotational solid by integrating the area of a slice. The AP Calculus resource works through an example of finding the volume of a solid created by rotating a function about the x-axis. The presentation breaks the...

In this trigonometric functions worksheet, high schoolers solve 8 multiple choice and graphing problems.  Students graph trigonometric functions given an equation and match graphs to a given scenario.

In this graphing  worksheet, students graph one sine equation.  A blank grid is provided.

Consign yourself to graphing cosine. Pupils graph the cosine function by first creating a table of values. They see the completed graph, consider the sinusoidal nature of the graph, and identify key features.