17.2 CHAPTER 17. TRIGONOMETRY
5-5-390-420 -210-240-270-300-330-360 -30-60-90-120-150-180 30 60 90 120 150 180 210 240 270 300 330360 390 420Figure 17.6: The graphof f(θ) = tan(θ + 30◦) (solid lines) and the graph of g(θ) = tan(θ) (dotted
lines).
Exercise 17 - 6
On the same set of axes, plot the following graphs:
- a(θ) = tan(θ− 90 ◦)
- b(θ) = tan(θ− 60 ◦)
- c(θ) = tan θ
- d(θ) = tan(θ + 60◦)
- e(θ) = tan(θ + 180◦)
Use your results to deduce the effect of p.
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You should have foundthat the value of p once again affects the y-intercept and phase shift of the
graph. There is a horizontal shift to the left if p is positive and to the right if p is negative.
These different properties are summarised in Table 17.6.
Table 17.6: Table summarising general shapes and positions of graphs of functions of the form y =
tan(θ + p). The curve y = tan(θ) is plotted with a dottedline.
k > 0 k < 0
Domain and Range
For f(θ) = tan(θ+p), the domain for one branch is{θ : θ∈ (− 90 ◦−p;90◦−p} because the function
is undefined for θ =− 90 ◦− p and θ = 90◦− p.
The range of f(θ) = tan(θ + p) is{f(θ) : f(θ)∈ (−∞;∞)}.