Cambridge Additional Mathematics

202 The unit circle and radian measure (Chapter 8)

Opening problem

Consider an equilateral triangle with sides 2 cm long. Altitude AN

bisects side BC and the vertical angle BAC.

Things to think about:

a Can you use this figure to explain why sin 30±=^12?

b Use your calculator to find the value of:

i sin 150± ii sin 390± iii sin(¡ 330 ±)

c Can you explain each result inb, even though the angles are

not between 0 ±and 90 ±?

DEGREE MEASUREMENT OF ANGLES

We have seen previously that one full revolution makes an angle of 360 ±, and the angle on a straight line

is 180 ±.

Onedegree, 1 ±,is 3601 th of one full revolution.

This measure of angle is commonly used by surveyors and architects.

RADIAN MEASUREMENT OF ANGLES

An angle is said to have a measure of oneradian, 1 c, if it is subtended

at the centre of a circle by an arc equal in length to the radius.

The symbol ‘c’ is used for radian measure but is usually omitted.

By contrast, the degree symbol isalwaysused when the measure

of an angle is given in degrees.

From the diagram below, it can be seen that 1 cis slightly smaller

than 60 ±. In fact, 1 c¼ 57 : 3 ±.

The word ‘radian’ is an abbreviation of ‘radial angle’.

A RADIAN MEASURE

30 ° 30 °

60 ° 60 °

A

BCN

2 cm

1 cm

radius¡¡=r

arc

length=r¡

1 c

r

r

60°

1 c

cyan magenta yellow black

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_08\202CamAdd_08.cdr Monday, 6 January 2014 11:40:10 AM BRIAN