Chapter 22

Trigonometric waveforms

22.1 Graphs of trigonometric functions

Bydrawinguptablesofvaluesfrom0◦to 360◦, graphs
ofy=sinA,y=cosAandy=tanAmay be plotted.
Values obtained with a calculator (correct to 3 deci-
mal places – which is more than sufficient for plotting
graphs), using 30◦intervals, are shown below, with the
respective graphs shown in Figure 22.1.

(a) y=sinA

A 0 30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦

sinA 0 0. 500 0. 866 1. 000 0. 866 0. 500 0

A 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦

sinA − 0. 500 − 0. 866 − 1. 000 − 0. 866 − 0. 500 0

(b) y=cosA

A 0 30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦

cosA 1. 0000. 8660. 5000 − 0. 500 − 0. 866 − 1. 000

A 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦

cosA − 0. 866 − 0. 500 0 0. 500 0. 866 1. 000

(c) y=tanA

A 0 30 ◦ 60 ◦ 90 ◦ 120 ◦ 150 ◦ 180 ◦

tanA 0 0. 577 1. 732 ∞ − 1. 732 − 0. 577 0

A 210 ◦ 240 ◦ 270 ◦ 300 ◦ 330 ◦ 360 ◦

tanA 0. 577 1. 732 ∞ − 1. 732 − 0. 577 0

2 1.0

24

2 0.5

2 1.0

22

0.5

1.0

2 0.5

0 30 60 90 120 150 180 210 240 270 300 330 360

30 60 90 120 180 210 240 270 300 360

30 60 90 120 150 180 210 240 270 300 330 360

(a)

1.0

0.5

0

(b)

(c)

4

2

0

150 330

y

y

y

y 5 tan A

y 5 cos A

A 8

A 8

A 8

y 5 sin A

Figure 22.1

From Figure 22.1 it is seen that

(a) Sine and cosine graphs oscillate between peak

values of±1.

(b) The cosine curve is the same shape as the sine

curve but displaced by 90◦.

(c) Thesineandcosinecurvesare continuousandthey

repeat at intervals of 360◦and the tangent curve

appearstobediscontinuousandrepeatsatintervals

of 180◦.

DOI: 10.1016/B978-1-85617-697-2.00022-3