Question

determine the number of cycles each sine function has in the interval from 0 to 2(pi). Find the amplitude and period of each function​

Answer 1

Answer:

A. cycles: 3

B. cycles: 1/2

A. amplitude: 2

B. amplitude: 1

A. period: 2/3 π

B. period: 4 π

Step-by-step explanation:

The sine function completes a cycle when it intercepts twice x-axis. For function in figure A, this happens 3 times, and for function in figure B we can only see half of a cycle between x = 0 and x = 2π

Amplitude is half of the distance between function maximum and minimum. For function in figure A, the maximum is 2 and the minimum is -2, then its amplitude is (2 - (-2))/2 = 2.

For function in figure B, the maximum is 1 and the minimum is -1, then its amplitude is (1 - (-1))/2 = 1.

Period is the distance between two maximums. For function in figure A, that distance is two intervals of the x-axis division. Each interval is 1/3 π long, then the period is 2/3 π.

Given that function in figure B makes half of a cycle between 0 and 2π, then 2π represents half of the period of the function, which is 2*2π = 4π