Cambridge International AS and A Level Mathematics Pure Mathematics 1

P1^

7

Other trigonometrical functions

ACTIvITy 7.3  Figure 7.33 shows the graphs of y = sin x and y = 2 + sin x for 0°  x  360°.

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

y = 2 + sin x.

Complete this statement.

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

ACTIvITy 7.4  Figure 7.34 shows the graphs of y = sin x and y = sin (x − 45°) for 0°  x  360°.

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

y = sin (x − 45°).

Complete this statement.

‘In general, the curve y = f(x − t) is obtained from y = f(x) by ... .’

–1

(^0) 90° 180° 270° 360° x
2
1
y
y = sin x
y = 2 + sin x
3
Figure 7.33
If you have a graphics
calculator, use it to
experiment with other
curves like these.
–0.5
(^0) 90° 180° 270° 360° x
1
0.5
y
y = sin x
–1 y = sin (x – 45°)
Figure 7.34
If you have a graphics
calculator, use it to experiment
with other curves like these.