Cambridge Additional Mathematics

-1

-0.5

x

0.5

1

y x

y=sin_&^* 3

-7 -6 -5 -4 -3 -2 -1 1234567

y

x

¼ 2 ¼ 3 ¼

1

-3

Trigonometric functions (Chapter 9) 253

2 Findbgiven that the function y= sinbx, b> 0 has period:

a ¼ 3 b 12 ¼

3 State the minimum and maximum values of:

a y= 5 sinx¡ 3 b y= 3 cosx+1 c y= 4 cos 2x+9

4 On the same set of axes, for the domain 06 x 62 ¼, sketch:

a y= cosx and y= cosx¡ 3 b y= tanx and y= 2 tanx

d y= sinx and y= 3 sinx+1

5 The function y=asinbx+c, a> 0 , b> 0 , has amplitude 2 , period ¼ 3 , and principal axis

y=¡ 2.

a Find the values ofa,b, andc. b Sketch the function for 06 x 6 ¼.

6 Consider the function y= 2 tanx.

a State a function which has the same shape, but has principal axis y=2.

b Draw y= 2 tanx and your function fromaon the same set of axes, for ¡ 2 ¼ 6 x 62 ¼.

7 Consider y= sin(x 3 ) on the domain ¡ 76 x 67. Use the graph to solve, correct to 1 decimal

place:

a sin(x 3 )=¡ 0 : 9 b sin(x 3 )=^14

8 Findmandngiven the following graph of the function

9 Solve for 06 x 62 ¼:

a sin^2 x¡sinx¡2=0 b 4 sin^2 x=1

10 Simplify:

a cos^3 μ+ sin^2 μcosμ b

cos^2 μ¡ 1

sinμ

c 5 ¡5 sin^2 μ d

sin^2 μ¡ 1

cosμ

y=sin_&^*x

3

-1-1

-0.5-0.5

xx

0.50.5

11

yy

-7-7 -6-6 -5-5 -4-4 -3-3 -2-2 -1-1 OO 11 22 33 44 55 66 77

y=sin( )Ve

c y= cosx and y= cos 2x+1

y= 2 sinmx+n:

4037 Cambridge

cyan magenta yellow black Additional Mathematics

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Y:\HAESE\CAM4037\CamAdd_09\253CamAdd_09.cdr Tuesday, 28 January 2014 9:45:49 AM BRIAN