Question

Consider the function f(x)= cos(x) which has an amplitude of 1 and a period of 2Pi. What modification to the function rule would cause the ampltiude to become 1/30 and the period to become 2Pi/5.

Answer 1

To change the amplitude of f(x) = cos(x) to 1/30 and period to 2π/5, multiply the function by 1/30 for the amplitude and by 5 in the argument for the period, resulting in the modified function f(x) = (1/30)cos(5x).

Step-by-step explanation:

To modify the function f(x) = cos(x), which has an amplitude of 1 and a period of 2π (2 Pi), so that the amplitude becomes 1/30 and the period becomes 2π/5, we would need to make two adjustments to the equation:

• The amplitude is adjusted by multiplying the function by the new amplitude, in this case, 1/30. So we replace cos(x) with (1/30)cos(x).
• To achieve the new period of 2π/5, we need to increase the frequency of the function by a factor that relates the old period to the new period. The function cos(x) has a period of 2π, so to change the period to 2π/5, we multiply the argument of the cosine function by the reciprocal of the fraction 2π/(2π/5) = 5. The function will now be (1/30)cos(5x).

Therefore, the modified function is f(x) = (1/30)cos(5x).