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Graph of sine
This animation shows how the graph of the sine function is born. A detailed explanation is found after the animation.
Click on the rocket button to zoom out. To zoom back in, press Option (Mac) or ALT (Windows) and click on the rocket button.
The graph of the sine function is constructed as follows:
| 1. | Recall that the value of the sine function at t is the y-coordinate of a point (x, y) on the unit circle that corresponds to t. This point rotates counterclockwise on the circle, starting at (1, 0). |
| 2. | Draw a vertical line segment from (x, y) onto the x-axis. The signed length of this vertical line segment represents the value of the sine function at t. Signed length mean that, if the vertical line segment is above the x-axis, we say that the length is positive; if below the x-axis, it is negative. |
| 3. | To the right of the unit circle, think of the extension of the x-axis as a new t-axis that corresponds to the value of an angle in the unit circle. |
| 4. | Horizontally transfer the vertical line segment from the unit circle to the position corresponding to the value of t on the t-axis. |
| 5. | When this transfer is repeated from t = 0 to t = 2π, the tip of the vertical line segment gives a trace of the values of the sine function in the ty-plane. (The horizontal axis is t and the vertical axis is y.) |
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Disclaimer • Updated August 20, 2008
Email: mitsuma@kutztown.edu