Question

If the function y=sinx is transformed to y=3sin(1/2x), how do the amplitude and period change?

Answer 1

When the function y = sin(x) is transformed to y = 3sin((1/2)x), the amplitude increases to 3 and the period increases to 4π.

Step-by-step explanation:

The function y = sin(x) represents a sine wave with an amplitude of 1 and a period of 2π.

When the function y = sin(x) is transformed to y = 3sin((1/2)x), the amplitude is multiplied by 3, resulting in an amplitude of 3. The period is divided by 1/2, resulting in a period of 4π.

So, the amplitude increases to 3 and the period increases to 4π when the function y = sin(x) is transformed to y = 3sin((1/2)x).