Question

are sinx and sin5x both bound by -1 and 1?

Answer 1

yes

Answer 2

why? i don't understand

Answer 3

The period of the function ( the rate at which the function cycles through all of it's values ranging from 1 to -1, twice ), is affected by the 5.

To change the magnitude or size of the sine wave, you need a constant coefficient multiplying in front.\[\Large \color{orangered}{A} \sin x, \qquad\qquad\qquad \color{orangered}{B} \sin 5x\]
The first function would range from A to -A because it's being multiplied by A
while the second function ranges from B to -B.

Answer 4

So maybe this would make more sense.
\[\Large \sin x, \qquad\qquad\qquad \color{orangered}{5}\sin x\]The second function will go up to 5 and down as far as -5 because of the change in magnitude.