Lean a ladder against the wall to create an angle. Class members use an interactive application to determine the angle a ladder makes with the ground. Individuals respond to five questions using inverse trigonometric functions.

When is the trigonometric value of a negative angle the same as the positive angle? Pupils compare the values of trigonometric functions for different angles and their negatives. The interactive resource provides a visual display to make...

Is there a relationship between the sign of sine and cosine and the angle on the unit circle? Scholars use an interactive to see the value of sine and cosine within different quadrants. they then use the information to determine the...

Go around the unit circle and create triangles. Pupils move a point around the unit circles to visualize the triangle associated with the angle in standard position. The three main trigonometric functions are defined in terms of the legs...

Spin through the trigonometric functions. Scholars determine the angle of rotation a snowboarding snowman makes at various distances in his jump. The class members then calculate the values of trigonometric functions for those angles.

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...

Climb the ladder to trigonometry. The interactive introduces trigonometric ratios and finding lengths of sides of right triangles created by a ladder and a building. Learners use the interactive to create triangles by moving the top of...

How far is that boat from the lighthouse? Scholars create diagrams to represent a scenario given the angle of depreciation from a lighthouse to a boat. Learners apply the basic trigonometric functions to find various distances...

How does the equation of a function reflect translations? Scholars manipulate the starting point of the parent square root function before determining the new equations that result from the translations. Class members also determine the...

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...

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....

Get a better understanding of the trigonometric functions by taking a look at the flip side. Pupils create angles within a unit circle and compare the values of the standard trigonometric functions to their reciprocal functions. The...

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...

Who needs a plan — let trigonometry protect you! Pupils determine the angle of an approaching enemy to a village wall. The scholars determine the exact value of trigonometric functions for the angle. Class members use trigonometry to...

A steal of a deal — get four angles for the value of one. An interactive resource allows individuals to visualize all four angles that have the same reference angle. Pupils answer questions by using the interactive to create the...

Determine the length of a falling ladder. Pupils use an interactive to find the angle a ladder makes with the floor after it falls to answer questions. The scholars use the triangle formed in the interactive to determine values of...

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...

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...

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...

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.

How do degrees relate to radians? The interactive allows pupils to manipulate the size of an angle in a unit circle to help see that relationship. Users determine the radian measure for given degree measures of angles, realizing 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.

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.