# How to plot and generate sine wave

• Dec 28th 2012, 11:13 PM
bungouk
How to plot sine wave and generate table
Hi All,

Could someone tell me how to plot the graph and generate the table for y = 9 sin (Ɵ - 15) over 360 degree.

The coordinates need to be a 15 degree intervals

regards

Bungouk
• Dec 28th 2012, 11:31 PM
chiro
Re: How to plot and generate sine wave
Hey bungouk.

Are you aware of the taylor series for the sine function (in radians)? Do you know how to convert radians to degrees (or degrees to radians)?
• Dec 28th 2012, 11:34 PM
bungouk
Re: How to plot and generate sine wave
i'm not aware of the taylor series and yes i do know how to convert degrees to radians and and radians to degrees
• Dec 28th 2012, 11:49 PM
chiro
Re: How to plot and generate sine wave

Trigonometric functions - Wikipedia, the free encyclopedia
• Dec 29th 2012, 12:22 AM
BobP
Re: How to plot and generate sine wave
Are you not allowed to use a scientific calculator, or even to look them up in tables ??????
• Dec 29th 2012, 12:30 AM
bungouk
Re: How to plot and generate sine wave
yes i am allowed to as long as i show it on graph and a table
• Dec 29th 2012, 02:37 AM
Prove It
Re: How to plot sine wave and generate table
Quote:

Originally Posted by bungouk
Hi All,

Could someone tell me how to plot the graph and generate the table for y = 9 sin (Ɵ - 15) over 360 degree.

The coordinates need to be a 15 degree intervals

regards

Bungouk

Don't bother using Taylor Series for this problem. You are expected to know the exact values of the sine of multiples of 30 degrees, and the others can be found using a half angle identity.
• Dec 29th 2012, 07:41 AM
bungouk
Re: How to plot sine wave and generate table
does the 9 represent the amplitude, what do i do with (Ɵ - 15) part
• Dec 29th 2012, 08:02 AM
skeeter
Re: How to plot and generate sine wave
Quote:

Originally Posted by bungouk
yes i am allowed to as long as i show it on graph and a table

then get out your calculator and make a table ... sketch the coordinates on graph paper.
• Dec 29th 2012, 08:09 AM
HallsofIvy
Re: How to plot and generate sine wave
So, what, exactly is the question? If it is, as you initially said, to "graph and generate the table" with "15 degree intervals", then you just need to use your calculator (make sure it is set to "degree" measure, not radian) to to take $\theta= 0, 15, 30, 45, ... 345, 360$ so that $\theta- 15= -15, 0, 15, 30, ... 330, 345$ and so find 9sin(-15), 9 sin(0), 9 sin(15), 9 sin(30), 9 sin(45), ..., 9 sin(330), 9 sin(450) and plot those points.

If, however, the problem is to use the "standard" graph, y= sin(x), and alter it to give y= 9 sin(x- 15), then, yes, "9" is the amplitude: sin(x) is always between-1 and 1 so that, no matter what $\theta$ is, 9 sin(x- 15) is always between -9 and 9. One thing you could do is draw horizontal lines at y= -9 and y= 9 as guides. You know, I presume, that sin(x) is periodic with period 360 degrees, that it is 0 when x= 0, goes up to 1 when x= 90, down to 0 at x= 180, down to -1 at x= 270, back up to 0 at x= 360 and then repeats. Okay, when $\theta- 15= 0$, that is, when $\theta= 15$, $9sin(\theta- 15)$ is 0. When $\theta- 15= 90$, that is, when $\theta= 105$, $9sin(\theta - 15)$ is 9, when $\theta- 15= 180$, that is, when $\theta= 195$, [tex]9sin(\theta-15)= 0[k/tex], etc.
• Dec 29th 2012, 08:46 AM
bungouk
Re: How to plot and generate sine wave
Plot on a single sheet of graph paper the two following functions over 360o. Ensure both your axis are clearly labelled and that the graph is appropriately titled. Produce tables to generate all of the coordinates for both functions at approximately 15o intervals.

a) Y = 9 sin (θ – 15)
b) Y = 5 cos (θ + 10)

• Dec 29th 2012, 09:13 AM
skeeter
Re: How to plot and generate sine wave
Quote:

Originally Posted by bungouk
Plot on a single sheet of graph paper the two following functions over 360o. Ensure both your axis are clearly labelled and that the graph is appropriately titled. Produce tables to generate all of the coordinates for both functions at approximately 15o intervals.

a) Y = 9 sin (θ – 15)
b) Y = 5 cos (θ + 10)

• Dec 29th 2012, 11:11 AM
Deveno
Re: How to plot and generate sine wave
taking the sine of θ - 15, is what's known as a "phase shift".

since you are going to find sine in 15 degree intervals anyway: do this:

sin(0°) = sin((15-15)°) <---this is your value for θ = 15°
sin(15°) = sin((30-15)°) <--this is your value for θ = 30°
etc.

remember to multiply everything by 9 when you're done. your answers will be numbers between -9 and 9 (if you get something of bigger absolute value than this, you've made a mistake, somewhere).

some points are "easy" to find (all angles are in degrees):

9sin(45-15) = 9sin(30) = 9/2 = 4.5

9sin(60-15) = 9sin(45) = 9√2/2 ~ 6.364

9sin(75-15) = 9sin(60) = 9√3/2 ~ 7.794

9sin(105-15) = 9sin(90) = 9

and so on. the "hard ones" to do are for θ = 30 and θ = 90 (which require finding sin(15) and sin(75)). after that, there is a pattern:

A,B,C,D,E,F,G (for the first 7 15-degree increments, starting with θ = 15)
F,E,D,C,B,A (for the next 6)
-B,-C,-D,-E,-F,-G (for the next 6)
-F,-E,-D,-C,-B (the next one would be A = 9sin(375-15) = 9sin(360) = 9sin(0) = 9sin(15-15), you've come "full circle").
• Dec 30th 2012, 10:44 PM
ibdutt
Re: How to plot sine wave and generate table
Just draw the curve for sine function.
Now you have to make adjustments as explained:
For the function f(x) = A sin(Bx + C ) + D
A gives the amplitude, B the period, C the horizontal shift and D the vertical shift. I am sure this would help you.