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 30 and the period to become 10Pi.

Answer 1

To achieve an amplitude of 30 and a period of 10Pi, modify the function to f(x) = 30 cos(x/5).

Step-by-step explanation:

To modify the function f(x) = cos(x) to have an amplitude of 30 and a period of 10Pi, you need to adjust the coefficient in front of the cosine function for the amplitude and the coefficient inside the function that affects the period. The general form of a sine or cosine function is A cos(Bx + C) + D, where A is the amplitude, and the period is given by 2Pi/B. To get an amplitude of 30, we multiply the cosine function by 30. To alter the period to 10Pi, we need to find B such that 2Pi/B = 10Pi, which simplifies to B = 1/5. Thus, the modified function should be f(x) = 30 cos(x/5).