Exercise 153 Page 423

Practice makes perfect

a Let's have a look at the general equation for a sine curve.

y&= asin[ b(x- h)]+k [0.5em] a&=amplitude b&=period h&=horizontal translation k&=vertical translation

Examining the given equation, we notice that the sine curve has a period that is twice the length of its parent function, y=sin x. Since the parent function has a period of 2π, the given function must have a period of 4π.

Finally, we have to translate the function to the right by π units.

b Examining the equation, we see that it has an amplitude of 10. Let's start by showing this transformation.

Next, we will calculate the period.

Period=2π/b

Substitute

b= 3

Period=2π/3

The period should be 2π3.

Finally, we have to vertically translate the curve by 2 units in the negative direction.

c Let's have a look at the general equation for a cosine curve.

y&= acos[ b(x- h)]+k [0.5em] a&=amplitude b&=period h&=horizontal translation k&=vertical translation

Examining the equation, we see that it has an amplitude of 5. Let's start by showing this transformation.

Finally, we have to horizontally translate the graph to the left by π4 units.

d Examining the given equation, we notice that the cosine curve has a period that is half that of its parent function, y=cos x. Since the parent function has a period of 2π, the given function must have a period of π.