Lesson 6, Topic 1
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Angle of Rotation

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 Rotation is often called turning. Rotation can be clockwise or anticlockwise as illustrated by the arrows below.

clock

A degree is a small measure of angle.

a) There are 360 degrees (i.e.  

360 degrees

Angle 360º is also called a full rotation or complete revolution or turn.

b) Half of a rotation  =  ½ of   360º  =  180º.

180 degrees

c) Quarter of a revolution ¼ of 360 =  90º

90 DEGREES

When two lines meet at an angle of 90º then both lines are said to be perpendicular to each other.

d) Three-quarter of a revolution  =   ¾  of 360   =  270º

270 degrees

Example:

a) How many degrees in 1 ¾ revolutions?

b) Find the number of revolutions in 

(i)    1200º

(ii)   108º

Solution

a) \( \scriptsize 1 \frac{3}{4} = \normalsize \frac{7}{4} \)

1 revolution    =  360º

So 7/4 revolution = \( \frac{7}{4} \scriptsize \: \times \: 360^o \\ = \scriptsize 7 \: \times \: 90^o \\ \scriptsize = 630^o \)

b) 360º = 1 revolution 

So, 1º  =   \( \frac{1}{360} \scriptsize \: revolutions \)

i) 1200º = \( \frac{1}{360} \scriptsize \: \times \: 1200 \\= \frac{120}{36} \\ = \frac{10}{3} \scriptsize \: revolutions \)

ii) 108º = \( \frac{1}{360} \scriptsize \: \times \: 108 \\ =\frac{108}{360} \\ = \frac{3}{10} \scriptsize \: revolutions \)

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