This unit introduces the six basic trigonometric functions, both as ratios of side lengths of right triangles and then transitioning to their definitions based on "wrapping" around a circle.
This lesson involves exploring the relationship between the central angle, the arc, and the radius of a circle.
This lesson involves the ratios of side lengths of triangles with invariant angle measures and the relationships to trigonometric functions of an angle.
Students will be able to describe the relationship between the unit circle and the sine and cosine functions. They will be also able to describe the shape of the sine and cosine curves after "unwrapping" the unit circle.
This lesson involves manipulating sliders to change the values of parameters in trigonometric functions and determining the effect that each change has upon the shape of the graph.
This lesson involves providing opportunities for students to explore and make sense of the graphs of the cotangent, secant, and cosecant functions.
This lesson involves examining graphs, or partial graphs, of sinusoidal functions to determine the values of their parameters and to express them in various ways involving sine and cosine functions.
Students will use a slider to animate the graphing of a function of time that models the height of a capsule on the London Eye observation wheel as the wheel turns. Students will discover the concepts of amplitude, frequency, period, and midline. Students will create an appropriate equation to model the height of a capsule on the wheel.
This lesson provides opportunities for students to explore the connections between the slope of a line and the tangent of the angle between the line and the horizontal.