1a. graph ( y=sin(x) ) over the interval ( -2pileq xleq2pi ).\n1b. how many cycles of the sine curve do you…
1a. graph ( y=sin(x) ) over the interval ( -2pileq xleq2pi ).\n1b. how many cycles of the sine curve do you see?
Answer
Explanation:
Step1: Recall the period of (y = \sin(x))
The period of the function (y=\sin(x)) is (T = 2\pi). A period (or cycle) is the length of one complete repetition of the sine - wave pattern.
Step2: Calculate the length of the interval
The interval is from (x=-2\pi) to (x = 2\pi). The length of the interval (L=2\pi-(-2\pi)=4\pi).
Step3: Divide the length of the interval by the period
Let (n) be the number of cycles. Using the formula (n=\frac{L}{T}), substituting (L = 4\pi) and (T=2\pi), we get (n=\frac{4\pi}{2\pi}=2).
Answer:
(2)