Cambridge Additional Mathematics

(singke) #1
The unit circle and radian measure (Chapter 8) 223

5aState the value ofμin:
i degrees ii radians.
b State the arc length AP.
c State the area of the minorsectorOAP.

6 Show that cos(^34 ¼)¡sin(^34 ¼)=¡

p
2.

7 If cosμ=¡^25 , ¼ 2 <μ<¼ find the otherfivetrigonometric ratios exactly.

8 Without using a calculator, evaluate:
a tan^260 ±¡sin^245 ± b cos^2 (¼ 4 ) + sin(¼ 2 ) c cos(^53 ¼)¡tan(^54 ¼)

9 Find two angles on the unit circle with 06 μ 62 ¼, such that:
a cosμ=^23 b sinμ=¡^14 c tanμ=3

10 Find the perimeter and area of a sector of radius 11 cm and angle 63 ±.

11 Find the radius and area of a sector of perimeter 36 cm with an angle of^23 ¼.

12 Simplify:
a sin(¼¡μ)¡sinμ b cosμtanμ

13 If sec®=¡ 313 and 0 <®<¼, find the otherfivetrigonometric ratios exactly.

14 Three circles with radiusrare drawn as shown,
each with its centre on the circumference of the
other two circles. A, B, and C are the centres of
the three circles.
Prove that an expression for the area of the shaded

region is A=
r^2
2
(¼¡

p
3).

O

1

1

q
A

P

A B

C

4037 Cambridge
cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_08\223CamAdd_08.cdr Monday, 23 December 2013 1:59:48 PM BRIAN

Free download pdf