HSC Together Year 12 Maths Advanced: Transformations of Trigonometric Functions

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• Trigonometric Functions
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# Transformations of Trigonometric Functions

This is part of the HSC Mathematics Advanced course under the topic Trigonometric Functions and sub-part Trigonometric Functions and Graphs. In this post, we will examine and apply transformations to sketch trigonometric functions of the form y=kf(a(x+b))+c , where a,b,c and k are constants, in a variety of contexts, where f(x) is one of \sin x, \cos x or \tan x , stating the domain and range when appropriate:

• Use technology or otherwise to examine the effect on the graphs of changing the amplitude (where appropriate), kf(x) , the period, y=f(ax) . the phase, y=f(x+b) , and the vertical shift, y=f(x)+c
• Use k, a, b, c to describe transformational shifts and sketch graphs

### Transformations of Trigonometric Functions

In this video, we will examine and apply transformations to functions, and see how the amplitude and period of a function can be affected and how a trigonometric function is vertically or phase-shifted.

### Sine and Cosine

Here, the graphing transformations are directly applied to the trigonometric functions of sine and cosine. We take a look at how the amplitude and period of a trigonometric function can be affected, and how it is vertically or phase-shifted.

### Tangent and Cotangent

Here, the graphing transformations are directly applied to the trigonometric functions of tangent and cotangent. We take a look at how the amplitude and period of a trigonometric function can be affected, and how it is vertically or phase-shifted.

### Secant and Cosecant

Here, the graphing transformations are directly applied to the trigonometric functions of secant and cosecant. We take a look at how the amplitude and period of a trigonometric function can be affected, and how it is vertically or phase-shifted.

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