How do you find the equation of a trigonometric graph eg. sin, cos...just by looking at the actual graph?

Question

I dont need to know wat the graph will look like. I need to know wat the equation would be if u were looking at the graph

Answer 1

sin(x) passes through the origin, whereas cos(x) does not. sin(x) and cos(x) both have period 2pi. They both have maximum value 1 and minimum value -1.
If the maximum is not 1, but k, then the equation is of the form k sin(x) or k cos(x).
If the period is not 2pi, but 2m pi, then the equation is of the form sin(x / m) or cos(x / m).
If the absolute value of the maximum is not equal to the absolute value of the minimum, then the graph has been shifted up or down, making the function one of the form h + sin(x) or h + cos(x) with h either positive or negative.
If the period does not run from 0 to 2pi for sine or from -pi to pi for cosine, then the graph has been shifted right or left, making the function one of the form sin(x +/- p) or cos(x +/ q).

You need to start with an equation of the form:
y = a + b sin(kx + m) or y = a + b cos(kx + m), and determine the values of a, b, k and m from the features of the particular graph.

Answer 2

Okay, I have just gone thru this topic at school, my Additional Mathematics course, and I will try to recall:

y = 5 sin 2x + 3

Here, the 3 means the 0-axis of the science curve. So, instead of y=0, the curve will start from this particular line.

The 5 means the amplitude of the graph. So, in this case, the maximum y-axis will be y=8, since 5+3 = 8. And the minimum will be 3-5 = -2, y=-2

The 2 means the frequence of the curve. Here, 360 / 2 = 180, so the frequency will be 180 degree.

Answer 3

if x=0
y=sin0=0

x=pi/2
y=1
sin graph

try to see max min points.