Algebra II End-of-Course Exam Content Standards—Module: Trigonometric Functions
Successful students will be able to recognize and model periodic phenomena using trigonometric functions. They will understand the relationship among the unit circle, the geometric definitions of sine and cosine, and the degree and radian measures of angles and will apply this understanding to graph trigonometric functions, determine key characteristics of the functions and their graphs, and describe the effect of transformations on both the symbolic and graphical representations of the functions. There are a variety of types of assessment items including some that cut across the objectives in this standard and require students to make connections and solve rich contextual problems.
T1. Trigonometric Functions
a. Recognize periodic phenomena and determine key characteristics of such phenomena.
- Key characteristics include the period between repetitions, the frequency of the repetitions, and the range of values.
- Periodic phenomena include sound waves, length of daylight, and situations involving circular motion.
b. Use the relationship of the sine and cosine functions to a central angle of the unit circle to determine the exact trigonometric ratio of angles on the unit circle. (0º to 360º, 0 to 2π)
- Interpret the sine, cosine, and tangent functions corresponding to a central angle of the unit circle in terms of horizontal and vertical sides of right triangles based on that central angle.
c. Explain and use both degree and radian measure for angles.
- Convert between the degree and radian measure of an angle.
d. Represent trigonometric functions using tables, graphs, verbal statements, and equations. Translate among these representations.
- Use the unit circle to extend the domain of the sine and cosine functions to the set of real numbers.
e. Determine key characteristics of trigonometric functions and their graphs.
- Key characteristics include zeros, amplitude, period, phase shift, vertical shift, and asymptotes.
f. Describe the effect that changes in the parameters of an equation of a trigonometric function in the form, f(x) = A sin B(x - C) + D (or the similar cosine function) have on the shape and position of its graph.
- Identify changes in the period, amplitude, vertical shift, and phase shift for the function.
- Identify the zeros of a function that has a vertical shift of 0.
- Identify and describe the transformations (vertical shifts, phase shifts, stretches and compressions) that occur when parameters are changed in trigonometric functions.
g. Recognize, express, and solve problems that can be modeled using trigonometric or other periodic functions.
Example: Explain the difference between frequency modulation used in FM radio signals and amplitude modulation used in AM radio signals.
- Use Pythagorean identities for sine, cosine, and tangent to solve trigonometric equations and problems.
- Use inverse trigonometric functions to solve equations and problems.
- Solve problems in context that rely on trigonometric relationships.
- This includes using and interpreting appropriate units of measurement and precision for the given application.