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Graphing transformations of trigonometric functions
- Lesson: 1a27:03
- Lesson: 1b34:05
- Lesson: 1c19:26
- Lesson: 221:41
Graphing transformations of trigonometric functions
After learning all the graphs of basic trigonometric functions, in this lesson, we are going to go a little bit further on how the graphs will be transformed as the functions change. The general form for the equation of trig functions is y = f [B(x + c)] + D, where f refers the trig function; A refers to the amplitude/steepness; B represents the period of the graph; C refers to phase shift (left or right) and D represents vertical shift (up or down). We will learn how to graph the trig function for multiple periods; state the vertical displacement, phase shift, period and amplitude; and also find the domain and range of the transformed functions.
Basic Concepts: Combining transformations of functions, Sine graph: y = sin x, Tangent graph: y = tan x, Secant graph: y = sec x
Related Concepts: Ferris wheel trig problems, Tides and water depth trig problems, Spring (simple harmonic motion) trig problems
Lessons
- 1.For each trigonometric function:
(i) Graph the trigonometric function for one period.
(ii) State the vertical displacement, phase shift, period, and amplitude.
(iii) State the domain and the range.a)y=2sin4π(x+3)+1b)y=3sec(2πx−π)−1c)y=−2sin(4x+4π)−3 - 2.For the trigonometric function: y=−tan(3x−6π)
i) Graph the trigonometric function for two periods.
ii) State the domain and the range.
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26.
Graphing Trigonometric Functions
26.1
Sine graph: y = sin x
26.2
Cosine graph: y = cos x
26.3
Tangent graph: y = tan x
26.4
Cotangent graph: y = cot x
26.5
Secant graph: y = sec x
26.6
Cosecant graph: y = csc x
26.7
Graphing transformations of trigonometric functions
26.8
Determining trigonometric functions given their graphs