Cambridge Additional Mathematics

If or is negative,

your calculator will give

in the domain.

sin tan

0

μμ

μ

-___wp<μ<

PARAMETRIC

PLOTTER

The arrow

shows the angle that

your calculator gives.

green

-1 1 x

1 y

-1

• We

2.30

-1 1 x O

1 y

-1

-0.4

-0.412

O

-1 1 x

1 y

-1

-0.322

O

216 The unit circle and radian measure (Chapter 8)

Example 11 Self Tutor

Find two anglesμon the unit circle, with 06 μ 62 ¼, such that:

a sinμ=¡ 0 : 4 b cosμ=¡^23 c tanμ=¡^13

a sin¡^1 (¡ 0 :4)¼¡ 0 : 412

But 06 μ 62 ¼

) μ¼¼+0: 412 or

2 ¼¡ 0 : 412

) μ¼ 3 : 55 or 5 : 87

b cos¡^1 (¡^23 )¼ 2 : 30

But 06 μ 62 ¼

) μ¼ 2 : 30 or

2 ¼¡ 2 : 30

) μ¼ 2 : 30 or 3 : 98

c tan¡^1 (¡^13 )¼¡ 0 : 322

But 06 μ 62 ¼

) μ¼¼¡ 0 : 322 or

2 ¼¡ 0 : 322

) μ¼ 2 : 82 or 5 : 96

2 Find two anglesμon the unit circle, with 06 μ 62 ¼, such that:

a cosμ=¡^14 b sinμ=0 c tanμ=¡ 3 : 1

d sinμ=¡ 0 : 421 e tanμ=¡ 6 : 67 f cosμ=¡ 172

g tanμ=¡

p

5 h cosμ=¡p^13 i sinμ=¡

p 2

p

5

Discovery 2 Parametric equations

#endboxedheading

Usually we write functions in the form y=f(x).

For example: y=3x+7, y=x^2 ¡ 6 x+8, y= sinx

However, sometimes it is useful to expressbothxandyin terms

of another variablet, called theparameter. In this case we say

we haveparametric equations.

What to do:

1aUse the graphing package to plot

f(x,y):x= cost, y= sint, 0 ± 6 t 6360 ±g.

Use the same scale on both axes.

The use of parametric

equations is not required

for the syllabus.

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_08\216CamAdd_08.cdr Friday, 4 April 2014 12:57:02 PM BRIAN