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Graph of Sinx

Graph of sin x is a periodic function with period 2π. So we will draw the graph of y = sin (x) in the interval of [0,2π]. The graph of sine looks like this.In order to draw the graph of y=sin(x) we will use the following steps :
1) Draw a Y-axis with 0,1,-1 ...on it.
2) From the origin draw an X-axis.
a) if you want a graph in π then mark the points π/2, π,3π/2, 2π etc.
As we know that sin(π) = 0 so the the sine curve will intersect at π,2π,3π, etc.
b) If you want the graph on the number line then mark the points 1,2,3,4...and so on.
The sine curve will cut the X-axis at 3.14,6.28,etc.
In short in the graph, the value of 3.14 on the X-axis represents $180^{0}$ and 6.28 is equivalent to $360^{0}$ or 2π.
3) y = a sin(x) the amplitude 'a' is 1 so the curve will be up to (0,1). If y = 2 sin(x) then the amplitude will be 2, so the curve will be up to (0,2).
Here ask-math explains you the sine curve in radians only.
Step 1 : Draw Y-axis and mark the the points 0,1 and -1 as the amplitude for y = sin(x) graph is 1. Draw the x-axis from 0 and mark the points π,2π,3π...etc.
step 1 : how to graph y=sinx
Step 2: As sin(0) = 0 so sine graph starts from the origin or you can say that sine graph cuts the X-axis at (0,0).
And sin(π/2) = 1 which is maximum for this particular graph since the amplitude is 1 so the sine curve is up to [π/2,1].
similarly sin(3π/2) = -1 which is maximum along the negative Y-axis so the sine curve is up to [3π/2,-1].
Note : For y = 2 sin x, the amplitude is 2 and sin(π/2) = 1 so the sine curve is up to [π/2,2] on positive Y-axis and [3π/2,-2] on negative Y-axis.
Since the sin x is an increasing function, we obtain the graph of y=sin x in the interval of [0,π/2]. We draw the graph of y = sin x by using the fact that sin(π- x) = sin x . So finally, we draw it in the interval [π,2π], using the fact that sin(π + x) = -sin x which means that the graph of y = sin x in [π,2π] is the mirror image of the graph of y = sin x in [0,π].

Practice on graph of sinx

1) What is the period of y = 2 sin(x).
2) Write the amplitude of y = 3 sin (x).
3) Draw the graph of y = 2 sin(x).


11th grade math

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