Finding a period of a regular sine expression?
Okay, so a is obviously equal to 4, but when I attempted to find b, I got the wrong answer, and even though the right answer($\frac{\pi}{4}$) is right, I don't understand how to get it. I got $\frac{\pi}{2}$ from this method:
- $\frac{2\pi}{B} = 4$(where 4 is the size of a period)
- $2\pi = 4B$
- $\frac{2\pi}{4} = B$
- $\frac{\pi}{2} = B$
How could you possibly get $\frac{\pi}{4} = B$ as the value of b from this?
$\endgroup$2 Answers
$\begingroup$The period is how much we need to go through our independent variable so that our function will repeat in value, i.e. how much we need to go through our independent variable for a full cycle. You can view that as double the length from a midpoint to the next midpoint or the length of a crest to the next crest or bottom point to bottom point. It is not the length from a highest point (crest) to the next lowest point (trough), it is rather double that length. That length is $2(4)=8$, which you can figure out if you look at the period as double the length from midpoint to next midpoint or double the length from crest to the next through.
$\endgroup$ $\begingroup$From your graph it seems that the amplitude $a$ is $a=5$ and the period is $\tau=8$. Since the period of the $\sin X$ function is $T=2\pi$ for your function we have. $$ b\tau=2\pi \iff 8b=2\pi\iff b=\frac{\pi}{4} $$
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