Trigonometric Functions Teacher Resources

Determine the location of a point on a moving wheel. The task challenges groups to determine the horizontal and vertical locations of a point on the edge of wheel that is moving. Teams first determine a function that will model the...

What effect does changing a parameter have on the graph of a trigonometric function? Pupils use a Desmos applet to explore the general sine graph. They experiment changing different parameters and record the resulting change of the...

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...

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...

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...

Finding the inverse of trigonometric ratios is not the same as finding the reciprocal. The presentation introduces how to find the angle of a right triangle given sides. Part of a larger playlist on geometry, the video uses the inverse...

Patterns can be shifty! Find the pattern when shifting the graph of tangent. Pupils move the graph of tangent to different locations on the coordinate plane. They observe what happens to the function and its vertical asymptotes...

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...

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...

Need practice deriving trigonometric angle formulas? With this instructional activity, pupils derive the sum and difference formulas for cosine and tangent and the difference formula for sine. Scholars use the sine sum formula and...

How many times can eager mathematicians catch the waves? Pupils find the solutions of three different trigonometric equations. They then determine the effect of the slope of a line that intersects a trigonometric function and the number...

Use a triangle area formula that works when the height is unknown. The eighth installment in a 16-part series on trigonometry revisits the trigonometric triangle area formula that previously was shown to work with the acute triangles....

Chase a periodic moving limit. Learners graphically determine the limit of the tangent function at different input values. Using sliders, pupils find out whether the tangent function approaches the same value from the left and the right....

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...

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...

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...

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. 

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...

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...

Many phenomena in life are periodic in nature. A task-based lesson asks scholars to explore one of these phenomena. They collect data showing the sunrise time of a specific location over the period of a year. Using the data, they create...

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.

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...

Let's keep trigonometry simple. When given a cosine ratio, learners must use the clues about the quadrant to determine the sine and tangent ratios. The answer key has a complete worked-out solution to help guide pupils through the...

Transform your lesson for transforming functions. Scholars transform linear, quadratic, exponential, rational, and trigonometric expressions. They write their expressions to fit specific forms and identify the values of the resulting...