Cambridge International AS and A Level Mathematics Pure Mathematics 1

Trigonometry

P1^

7

(ii) The curve of y = 3 + cos x is obtained from that of y = cos^ x by a translation

0

3







.

The curve therefore oscillates between y = 4 and y = 2 (see figure 7.39).

(iii) The curve of y = cos (x − 60°) is obtained from that of y = cos x by a

translation of

60

0

 °





^ (see figure 7.40).

–1

x

0

90° 270°

y = cos x

180° 360°

1

y

1

2

3

4

0 90° 180° 270° x

y = 3 + cos x

360°

y

–1

x

0

90° 270°

y = cos x

180° 360°

1

y

1

2

3

4

0 90° 180° 270° x

y = 3 + cos x

360°

y

Figure 7.39

–1

x

0

90° 270°

y = cos x

180° 360°

1

y

–1

x

0

y = cos (x – 60°)

1

y

150° 330°

Figure 7.40