# Equation to graph a sine wave that acts like a point on a unit circle

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• btb4198
In summary, the conversation discusses the need for an equation to graph a sine wave that acts like a unit circle but only with positive numbers. The participant realizes that using the equation Y = A*sin(x)^2 should work, but the x value needs to be converted from radians to degrees. After some trial and error, the participant is able to successfully graph the desired wave. The conversation also touches on the topic of trigonometric identities and a follow-up question is mentioned.
btb4198
I need an equation to graph a sine wave that act like a unit circle but only positive numbers.
so I need it to be 0 at 0, A at 90 , 0 at 180, A at 270, 0 at 360, and A at 450 and so on and so on...

Now I know sin(0) is 0 in degrees and sin(90) 1
and I know if you Square a number is will always get you a positive number
so Y = A* sin(x)^2 should work, but x has to be in degrees, so you have to convert from radians to degrees.

with is 180/π

so now I have
Y = A * sin(x*(180/π) ^2
but this is not working on my computer's graphing Calculator:

I tried doing adding - 90
Y = A * sin(x*(180/π -90) ^2

but that did not work
I never trying adding 90, - 360 and 360 nothing is working.
why is this ? what am I missing ?
ago the graph should be 0 on 0, 180 , and 360 and should be A( in this case 5) only on 90, 270 and 450 and so on and so on

Last edited by a moderator:
Do you just want something like ##|sin(x)|##?

Also, your calculator probably assumes x is in radians to begin with, so when you try to convert it to degrees, you're shortening the period a lot more than you intended.

btb4198
Office_Shredder said:
Do you just want something like ##|sin(x)|##?

Also, your calculator probably assumes x is in radians to begin with, so when you try to convert it to degrees, you're shortening the period a lot more than you intended.
no that give me this:

I need it to go down on 90 and not 180

Try multiplying by ##\pi/180## instead of ##180/\pi## inside of the sine function to get the right conversion to degrees.

Office_Shredder said:
Try multiplying by ##\pi/180## instead of ##180/\pi## inside of the sine function to get the right conversion to degrees.
Thanks !
that work.

is it wrong then?
how you were right!
my graph is working on

btb4198 said:
I need an equation to graph a sine wave that act like a unit circle but only positive numbers.
so I need it to be 0 at 0, A at 90 , 0 at 180, A at 270, 0 at 360, and A at 450 and so on and so on...

Now I know sin(0) is 0 in degrees and sin(90) 1
and I know if you Square a number is will always get you a positive number
so Y = A* sin(x)^2 should work, but x has to be in degrees, so you have to convert from radians to degrees.

with is 180/π

so now I have
Y = A * sin(x*(180/π) ^2
but this is not working on my computer's graphing Calculator:
View attachment 290112

I tried doing adding - 90
Y = A * sin(x*(180/π -90) ^2

but that did not work
I never trying adding 90, - 360 and 360 nothing is working.
why is this ? what am I missing ?
ago the graph should be 0 on 0, 180 , and 360 and should be A( in this case 5) only on 90, 270 and 450 and so on and so on

From the basic trig identities \begin{align*} \cos^2 x+ \sin^2 x &= 1 \\ \cos^2 x - \sin^2 x &= \cos(2x) \end{align*} it follows that $\sin^2 x = (1 - \cos (2x))/2$. That's not what you want.

It sounds like what you want is $$y(x) = \frac{A}{2}\left(1 + \sin\left( \frac{\pi x}{180}\right)\right).$$

pasmith said:
From the basic trig identities \begin{align*} \cos^2 x+ \sin^2 x &= 1 \\ \cos^2 x - \sin^2 x &= \cos(2x) \end{align*} it follows that $\sin^2 x = (1 - \cos (2x))/2$. That's not what you want.

It sounds like what you want is $$y(x) = \frac{A}{2}\left(1 + \sin\left( \frac{\pi x}{180}\right)\right).$$
No
Office_Shredder was right...
I got the graph I wanted

## 1. What is the equation for graphing a sine wave that acts like a point on a unit circle?

The equation for graphing a sine wave that acts like a point on a unit circle is y = sin(x).

## 2. How does the equation y = sin(x) relate to a point on a unit circle?

The equation y = sin(x) represents the y-coordinate of a point on a unit circle, where the x-coordinate is the angle (in radians) along the circumference of the circle.

## 3. Can the equation y = sin(x) be used to graph a full circle?

Yes, by graphing y = sin(x) from 0 to 2π (or 0 to 360 degrees), the resulting curve will form a full circle with a radius of 1.

## 4. What is the period of the sine wave graphed by the equation y = sin(x)?

The period of y = sin(x) is 2π, meaning that the graph will repeat itself every 2π units along the x-axis.

## 5. How does the amplitude of y = sin(x) affect the graph?

The amplitude of y = sin(x) determines the height of the wave, and can stretch or compress the graph vertically. A larger amplitude results in a taller wave, while a smaller amplitude results in a shorter wave.

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