Sine and Cosine of Every Angle—Section 6.3—Day 1
For any angle drawn in standard position with (x, y) lying on the terminal
side at a non-zero distance ,
and
and
. This is how we define the sine and
cosine functions.
With this definition: we can find the sine and
cosine of EVERY angle.
The sine ratio of all coterminal angles is the
same. The cosine ratio of all coterminal angles is
the same.
When angles are related, then the sine and cosine
ratios are also related. The other trig functions
also repeat in this kind of pattern, but more on
that later.
Your book discusses the “wrapping function” which occurs when the radius equals 1. On this
unit circle, sin() = y and cos() = x. Some of you may have had the trig functions defined this
way in a previous class.
Advise: Study pages 506 to 513 of your book, and complete three tables as assigned here, use
your homework and study plan until you can find the cosine and sine of any angle and determine
if your results are at least in the correct quadrant. Here is the circle we used in class.
Goal: Find the sine or cosine of any angle, and understand the symmetry found in these
circular functions .