Algebra 2: Resources and Extra Practice - 9.03 Trigonometric Functions with Periodic Phenomena

Algebra 2: Resources and Extra Practice

9.03 Trigonometric Functions with Periodic Phenomena

Essential Question:

How are trigonometric functions graphed to show the period, midline, and amplitude?
How can a trigonometric function be chosen to model periodic phenomena with specified amplitude, frequency, and midline?
How does replacing f(x) with f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative) affect the graph?
How does a function model the relationship between two quantities?
What is the rate of change of a function over a specified interval?
How can a function fitted to data be used to solve problems?

Lesson 9.03 Video - If video does not load correctly, Click Here to watch the video.

Khan Academy Resources

Graph of y=sin(x)The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1]. See how we find the graph of y=sin(x) using the unit-circle definition of sin(x).

Features of sinusoidal functionsSal introduces the main features of sinusoidal functions: midline, amplitude, & period. He shows how these can be found from a sinusoidal function's graph.

Amplitude & period of sinusoidal functions from equationSal finds the amplitude and the period of y=-0.5cos(3x).

Graph of y=tan(x)Sal draws the graph of the tangent function based on the unit circle definition of the function.

Transforming sinusoidal graphs: vertical & horizontal stretchesSal graphs y=-2.5*cos(1/3*x) by considering it as a vertical stretch and reflection, and a horizontal stretch, of y=cos(x).

Trig word problem: modeling daily temperatureSal solves a word problem about the daily change in temperature by modeling it with a sinusoidal function.

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