Cambridge Additional Mathematics

220 The unit circle and radian measure (Chapter 8)

5 Without using a calculator, evaluate:

a sin^260 ± b sin 30±cos 60± c 4 sin 60±cos 30±

d 1 ¡cos^2 (¼ 6 ) e sin^2 (^23 ¼)¡ 1 f cos^2 (¼ 4 )¡sin(^76 ¼)

g sin(^34 ¼)¡cos(^54 ¼) h 1 ¡2 sin^2 (^76 ¼) i cos^2 (^56 ¼)¡sin^2 (^56 ¼)

j tan^2 (¼ 3 )¡2 sin^2 (¼ 4 ) k 2 tan(¡^54 ¼)¡sin(^32 ¼) l

2 tan 150±

1 ¡tan^2150 ±

Check your answers using your calculator.

Example 14 Self Tutor

Find all angles 06 μ 62 ¼ with a cosine of^12.

Since the cosine is^12 , we draw the

vertical line x=^12.

Because^12 is involved, we know the

required angles are multiples of¼ 6.

They are ¼ 3 and^53 ¼.

6 Find all angles between 0 ±and 360 ±with:

a a sine of^12 b a sine of

p

3

2 c a cosine of

p^1

2

d a cosine of¡^12 e a cosine of¡p^12 f a sine of¡

p

3

2

7 Find all angles between 0 and 2 ¼(inclusive) which have:

a a tangent of 1 b a tangent of¡ 1 c a tangent of

p

3

d a tangent of 0 e a tangent ofp^13 f a tangent of¡

p

3

8 Find all angles between 0 and 4 ¼with:

a a cosine of

p

3

2 b a sine of¡

1

2 c a sine of¡^1

9 Findμif 06 μ 62 ¼ and:

a cosμ=^12 b sinμ=

p

3

2 c cosμ=¡^1 d sinμ=1

e cosμ=¡p^12 f sin^2 μ=1 g cos^2 μ=1 h cos^2 μ=^12

i tanμ=¡p^13 j tan^2 μ=3

10 Findallvalues ofμfor whichtanμis: a zero b undefined.

x

y

Td_p

x=Qw

O Qw

e_p

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Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_08\220CamAdd_08.cdr Monday, 23 December 2013 1:59:11 PM BRIAN