Question

what is the amplitude of the sinusoid by y = -4cos(2x) ? Please try and do a step by step. Literally have no idea how to solve this D:

Answer 1

when you graph this, the amplitude tell you how far it goes up and down from the midline.

Answer 2

take the absolute value of the number in front of cosine

Answer 3

Brilliant :)
Let's start with the general form of the sinusoid, shall we?
\[\Large \color{red}a \cos(\color{green}px + \color{blue}b)+\color{orange}q\]

Answer 4

Note that in this example, you can replace the cos with sin, it doesn't really change the nature of these values :)

Answer 5

a is your amplitude, just always take the absolute value of a

Answer 6

^That it is :)
As precal has mentioned, the amplitude is the 'height' of your graph (WARNING: This is NOT always the highest value that y could take. See "Vertical Shift" for details)

To get the amplitude once your sinusoid is of this form...
\[\Large \color{red}a \cos(\color{green}px + \color{blue}b)+\color{orange}q\]

As @precal has already mentioned, the amplitude is given by
\[\Large |\color{red}a|\]

Answer 7

Sooner or later, you might be asked for what's called the PERIOD of the sinusoid. Period is how long (on the x-axis) before your sinusoid begins to REPEAT itself. The period itself is given by this expression:
\[\Large \frac{2\pi}{\color{green}|p|}\]

Answer 8

I believe I stated that the amplitude is the distance of how far and how low the function is from the midline

Answer 9

q is your midline in this case it is zero

Answer 10

Warning wasn't meant to correct you @precal :)
It was for the OP