How do you graph $y = 2 sin (\frac{x}{2})$ $y=2sin(x/2)$ ?

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Answer 1 · 2018-05-14T10:39:01

Vertical and horizontal stretches.

Starting from the standard sine function $y = sin (x)$ $y=sin(x)$ , you have two transformations:

$sin (x) \to sin (\frac{x}{2})$ $sin(x) \to sin(x/2)$ . Multipling the input variable means to horizontally stretch/compress the graph of the function. So, in general, $f (x) \to f (k x)$ $f(x) \to f(kx)$ means to compress the graph if $| k | > 1$ $|k|>1$ , and stretch it otherwise. Since in your case $k = \frac{1}{2}$ $k = 1/2$ , the graph will be stretched by a factor of $2$ $2$ . This means, for example, that the sinusoidal waves will take twice the time to complete their oscillations.
Then, you have $sin (\frac{x}{2}) \to 2 sin (\frac{x}{2})$ $sin(x/2) \to 2sin(x/2)$ . This kind of transformations $f (x) \to k f (x)$ $f(x) \to kf(x)$ result in a vertical stretch if $| k | > 1$ $|k|>1$ , or a vertical compression otherwise. Since in your case $k = 2$ $k=2$ , the graph will be vertically stretched, again by a factor of $2$ $2$ . This affects the amplitude of the waves, which will no longer range between $- 1$ $-1$ and $1$ $1$ , but between $- 2$ $-2$ and $2$ $2$ .

Here,+2sin(x%2F2)) you can see the two graphs drawn together.

How do you graph y=2sin(x2)y=2sin(x/2)?