Still Confused?

Try reviewing these fundamentals first

Algebra

Combining transformations of functionsTrigonometry

Sine graph: y = sin xTrigonometry

Tangent graph: y = tan xTrigonometry

Secant graph: y = sec xStill Confused?

Try reviewing these fundamentals first

Algebra

Combining transformations of functionsTrigonometry

Sine graph: y = sin xTrigonometry

Tangent graph: y = tan xTrigonometry

Secant graph: y = sec xStill Confused?

Try reviewing these fundamentals first

Algebra

Combining transformations of functionsTrigonometry

Sine graph: y = sin xTrigonometry

Tangent graph: y = tan xTrigonometry

Secant graph: y = sec xNope, got it.

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Get Started Now- Lesson: 1a27:03
- Lesson: 1b34:05
- Lesson: 1c19:26
- Lesson: 221:41

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

- 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)$y = 2\sin \frac{\pi }{4}(x + 3) + 1$b)$y = 3\sec (\frac{\pi }{2}x - \pi ) - 1$c)$y = - 2\sin (4x + 4\pi ) - 3$ - 2.For the trigonometric function: $y = - \tan \left( {\;\frac{x}{3} - \frac{\pi }{6}\;} \right)$

i) Graph the trigonometric function for two periods.

ii) State the domain and the range.

23.

Graphing Trigonometric Functions

23.1

Sine graph: y = sin x

23.2

Cosine graph: y = cos x

23.3

Tangent graph: y = tan x

23.4

Cotangent graph: y = cot x

23.5

Secant graph: y = sec x

23.6

Cosecant graph: y = csc x

23.7

Graphing transformations of trigonometric functions

23.8

Determining trigonometric functions given their graphs

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