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
