Unit Circle

Sine

Picture
On the unit circle, sin equals y. It is positive in quad I and II, and is negative in quad III and IV.

Problem 1 (easy): Given the coordinates (√2/2, √2/2), determine the sine of the coordinates. 

 Problem 2 (medium): Given 4Π/3 R on the unit circle, find the coordinates and determine sine.


Problem 3 (hard): Explain why the coordinates for 60 degrees on the unit circle are (1/2, √3/2).


Problem 4 (applied): A suveyer is looking at a telephone pole. He knows it is 20 feet tall. He is looking at it from a 45 degree angle. Use sine to determine how far away he is from the top of the pole.