Cambridge International AS and A Level Mathematics Pure Mathematics 1

Trigonometry

250

P1^

7

(b) f : x  4 + 2 sin x

The maximum value of sin x is 1.

So the maximum value of f is 4 + 2 × 1 = 6.

The minimum value of sin x is −1.

So the minimum value of f is 4 + 2 × ( –1) = 2.

So the range of f is 2  f(x)  6.

(c) As a = 4 and b = 2,

y = a + b sin x is

y = 4 + 2 sin x.

Figure 7.42 shows the graph of

y = 4 + 2 sin x.

(ii) For a function to have an inverse it must be one-to-one.

The domain of g starts at π 2 and must end at^32 π, as the curve turns here.

So k =^3

π.

(^0) π π 2 π x
2
2
1
y
4
5
6
3
3π
2
Figure 7.42
2 π 2 π x
2
1
y
4 J
5

3
3π
2
π
2
Figure 7.43