Question

How many cycles does each sine function have in the interval from 0 to 2 pi. Find the amplitude and period of each function

Answer 1

Given: The graph of the sine function.

Required: To find the amplitude, period, and no of cycles of the given sine function in the interval 0 to 2pie.

Explanation: The given graph is

The sine function represented in the graph cycles once from 0 to 2pie, with a maximum of 3 and a minimum of -3.

Since the maximum value of given function is 3. Therefore the amplitude of the function is 3.

Also, the period of the given sine function is

`Period=2\pi`

Final Answer:

`\begin{gathered} Cycles=1 \\ Amplitude=3 \\ Period=2\pi \end{gathered}`