Question

Is y=cos(x/2) a vertical shrink or a horizontal shrink?

Answer 1

Here are both graphs

Answer 2

Thanks, I already know what they look like I just don't know when its a horizontal or vertical shrink

Answer 3

the so-called "horizontal shift" or "transformations" for the trig functions, occur when their "regular period" gets interrupted, either expanded or shrunk
so, sine and cosine have a "regular period" or \(2\pi\)
and you can get it by
$$
cos(x) = cos(1x)\\
period = \frac{2\pi}{1}
$$

Answer 4

now, what you have is really
$$
cos\pmatrix{\frac{x}{2}} = cos\pmatrix{\frac{1}{2}x}\\
period = \frac{2\pi}{\frac{1}{2}} \implies 4\pi
$$

Answer 5

so, the "normally \(2\pi\)" period, gets affected by the coefficient in front of the "x" variable in the expression, in this case, what would otherwise be a "normal \(2\pi \)" got stretched to a \(4\pi\)

Answer 6

I just wanted to know if it was a vertical or horizontal shrink I already know all that