Understanding Sine Function Through Unit Circle Graphing

TLDR; Graphing the sine function using the unit circle demonstrates how the sine values change with respect to angles.

⭕ Unit Circle and Sine Function

The unit circle's intersection with the terminal side of an angle provides the cosine and sine function values.

The x-coordinate represents the cosine function value, while the y-coordinate represents the sine function value.

The animation will demonstrate this point's movement around the unit circle and plotting of the sine function values on the coordinate plane.

🔄 Sine Function Values

The sine function value is zero when the angle is at 0 radians.

As the angle approaches pi/2 radians, the sine function value increases to +1, indicating an upward trend.

At pi/2 radians, the sine function value reaches 1, then decreases back to zero as the angle approaches pi.

The sine function value continues to decrease to -1 as the angle reaches 3pi/2, and then increases back to zero as the angle reaches 2pi.

This pattern represents one period of the sine function, and it repeats as the graph rotates around the unit circle.

🔄 Repetition of Sine Function Graph

The sine function graph repeats itself as the animation continues to rotate around the unit circle.

The values of the sine function start at zero, increase to one, decrease to zero, further decrease to -1, and then increase back to zero.

All these sine function values are derived from the y-coordinates of points on the unit circle.

Frequently asked questions

What does the unit circle demonstrate about the sine function?

The unit circle demonstrates how the sine values change with respect to angles, as the x-coordinate represents the cosine function value and the y-coordinate represents the sine function value.

At what angle is the sine function value zero?

The sine function value is zero when the angle is at 0 radians.

How does the sine function value change as the angle approaches pi/2 radians?

As the angle approaches pi/2 radians, the sine function value increases to +1, indicating an upward trend.

What pattern does one period of the sine function represent?

One period of the sine function involves the value starting at zero, increasing to one, decreasing to zero, further decreasing to -1, and then increasing back to zero.