1.6b day 2 Evaluating Trig Functions Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2008 President James A. Garfield National Historic Site Mentor, Ohio

First, a little review. Answer as quickly as you can!

First, a little review. Answer as quickly as you can!

We can find exact values for certain angles using special triangles. The first is the 45 o triangle. If we superimpose this triangle on a unit circle, the hypotenuse would have a length of 1, and the triangle would look like this: If we let the two perpendicular sides have a length of 1, then the hypotenuse is:

In calculus we frequently do not have to rationalize the denominator, so we can “cheat” and re-label the sides.

It is not a “unit” circle any more, but these labels let us quickly evaluate the trig functions. Move the triangle to find other values. You are welcome to rationalize the denominator any time you like!

Notice that in this position, the x coordinate is negative.

Here both the x and y coordinates are negative.

In this position, the y coordinate is negative.

It is great if you can memorize these or picture the unit circle or special triangles in your mind. However, a quick sketch and a correct answer is always better than a guess and a wrong answer! 