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.