Cambridge International AS and A Level Mathematics Pure Mathematics 1

Trigonometry

246

P1^

7

Reflections

ACTIvITy 7.5  Figure 7.35 shows the graphs of y = sin x and y = –sin x for 0°  x  360°.

Describe the transformation that maps the curve y = sin x on to the curve

y = –sin x.

Complete this statement.

‘In general, the curve y = –f(x) is obtained from y = f(x) by ... .’

One-way stretches

ACTIvITy 7.6  Figure 7.36 shows the graphs of y = sin x and y = 2 sin x for 0°  x  180°.

What do you notice about the value of the y co-ordinate of a point on the curve

y = sin x and the y co-ordinate of a point on the curve y = 2 sin x for any value of x?

Can you describe the transformation that maps the curve y = sin x on to the curve

y = 2 sin x?

±

 ƒ ƒ ƒ ƒ x





y

y sinx

y ±sinx



Figure 7.35

If you have a graphics

calculator, use it to experiment

with other curves like these.

If you have a graphics

calculator, use it to

experiment with other

curves like these.

0 x

y = 2 sin x

y = sin x

180°

1

2

y

Figure 7.36