Cambridge Additional Mathematics

222 The unit circle and radian measure (Chapter 8)

3 Find:

a sin 159± if sin 21±¼ 0 : 358 b cos 92± if cos 88±¼ 0 : 035

c cos 75± if cos 105±¼¡ 0 : 259 d sin(¡ 133 ±) if sin 47±¼ 0 : 731

4 Determine the area of a sector of angle^512 ¼and radius 13 cm.

5 Use the unit circle to findμsuch that cosμ=¡sinμ, 06 μ 62 ¼.

6 Find exact values for sinμ, cosμ, and tanμ forμequal to:

a 360 ± b^23 ¼ c ¡¼ d^83 ¼

7 If cosμ=^34 find the possible values of sinμ.

8 Evaluate:

a 2 sin(¼ 3 ) cos(¼ 3 ) b tan^2 (¼ 4 )¡ 1 c cos^2 (¼ 6 )¡sin^2 (¼ 6 )

9 Given tanx=¡^32 and^32 ¼<x< 2 ¼, find: a

10

Find the perimeter and area of the sector.

11 Suppose cosμ=

p

p^11

17 andμis acute. Find the exact value oftanμ.

12 Find all angles between 0 ±and 360 ±which have:

a a cosine of¡

p

3

2 b a secant of

p

2 c a cotangent of ¡p^13

13 Findμfor 06 μ 62 ¼ if:

a cosμ=¡ 1 b sin^2 μ=^34

14 If sinx=¡^14 and ¼<x<^32 ¼, find the otherfivetrigonometric ratios exactly.

Review set 8B

1 Convert these radian measurements to degrees:

a^25 ¼ b^54 ¼ c^79 ¼ d^116 ¼

2 Illustrate the regions where sinμ and cosμ have the same sign.

3 Use a unit circle diagram to find:

a cos(^32 ¼) and sin(^32 ¼) b cos(¡¼ 2 ) and sin(¡¼ 2 )

4 Suppose m= sinp, wherepis acute. Write an expression in terms ofmfor:

a sin(¼¡p) b sin(p+2¼) c cosp d tanp

4

1 c

cosx b sinx.

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100 4037 Cambridge
Additional Mathematics
Y:\HAESE\CAM4037\CamAdd_08\222CamAdd_08.cdr Friday, 24 January 2014 3:24:02 PM BRIAN