Cambridge International Mathematics

EXERCISE 29G.1

1aBy findingx-coordinates of points on the unit circle, copy and complete:

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

y= cosμ

b Useato graph y= cosμ for 0 o 6 μ 6360 o, making sure the graph is fully labelled.

c What is the maximum value of cosμ and when does it occur?

d What is the minimum value of cosμ and when does it occur?

2aBy using tanμ=

sinμ

cosμ

, copy and complete:

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

y= tanμ 0 p^13

p

3 und.

b

c

PROPERTIES OF BASIC TRIGONOMETRIC GRAPHS

Click on the icon to see how the graphs of y= sinμ, y= cosμ and y= tanμ are

generated from the unit circle.

Before we consider these graphs in more detail, we need to learn appropriate language for

describing them.

TERMINOLOGY

² Aperiodic functionis one which repeats itself over and over in a horizontal direction.

² Theperiodof a periodic function is the length of one repetition or cycle.

² The graph oscillates about a horizontal line called theprincipal axisormean line.

² Amaximum pointoccurs at the top of a crest.

² Aminimum pointoccurs at the bottom of a trough.

² Theamplitudeis the vertical distance between a maximum or minimum point and the principal

axis.

DEMO

period

amplitude

minimum point

maximum point

principal axis

Find the equations of the vertical asymptotes of y= tanμ for 0 o 6 μ 6360 o.

Useaandbto graph y= tanμfor 0 o 6 μ 6360 o.

596 Further trigonometry (Chapter 29)

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_29\596IGCSE01_29.CDR Monday, 27 October 2008 2:53:15 PM PETER