CHAPTER 17. TRIGONOMETRY 17.2
Table 17.2: Table summarising general shapes and positions of graphs of functions of theform
y = cos(kx). The curve y = cos(x) is plotted with a dottedline.
k > 0 k < 0Intercepts
For functions of the form, y = cos(kθ), the details of calculating the intercepts with the y axis are
given.
The y-intercept is calculated as follows:
y = cos(kθ)
yint = cos(0)
= 1Functions of the Formy=tan(kθ) EMBCV
In the equation, y = tan(kθ), k is a constant and has different effects on the graph of the function.
The general shape of the graph of functions ofthis form is shown in Figure 17.3 for the function
f(θ) = tan(2θ).
5
− 5
360 270 − 180 − − 90 − 90 180 270 36 0
Figure 17.3: The graphof f(θ) = tan(2θ) (solid line) and the graph of g(θ) = tan(θ) (dotted line).
The asymptotes are shown as dashed lines.
Exercise 17 - 3
On the same set of axes, plot the following graphs:
- a(θ) = tan0, 5 θ