The Unit Circle and Trigonometric Functions
- Albert Navetta
Drag the red circle, which is the terminal point for the arc of length on the unit circle. Here are some things to observe.
- and are the and coordinates of the terminal point of .
- The segment of the tangent line to the unit circle at the terminal point of between the -axis and -axis is of length . The segment also intersects the -axis at and the -axis at .
- Notice that very close to , , and become indistinguishable.
- By observing similar triangles and with a little algebra, you should be able to determine why , , , and .
- You should notice right triangles that show the Pythagorean identities , and . There are other too. See if you can find and prove them.