Question

Choose the equation of the graph shown.
y=-2cosx
y=-2sinx
y=2cosx
y= 2sinx

Answer 1

y = -2 sin x

Explanation:

As a basic,

y = cos x has a value of 1 at x = 0, and

y = sin x has a value of 0 at x = 0

Note: the value 1 can change to 2, 3, 4, etc. if the amplitude increases

Looking at the graph at x = 0, we see the y-value is 0, so definitely this is a sin graph. We can eliminate the cos choices.

So is it y = 2 sin x or y = -2 sin x??

If the graph goes downward from 0 (at x = 0), it is reflected of original, so that would be y = - sinx.

Since the graph decreases (goes downward) from x = 0, it is definitely the graph of negative sin. So y = - 2 sin x