Precalculus 1/20/10

Hey guys, it's Peyton with the first student post on the blog.

Today we learned how to use the unit circle. We also learned some equations that helped us utilize the unit circle.

Here are some of the equations we didn't learn in class:

Let's do some examples.

First, we'll see that pi over four is a first quartile 45-45-90 triangle. Looking at the equation for sin above, we know that we only need the y value. So, our answer is:

Just like the last problem, we'll first find the type of triangle we're dealing with. pi over three is a 60-30-90 right triangle. For cosine we need the x value, so our answer will be

Let's do one more example and mix it up a bit.

Before we flip out because its cotangent, let's remember that it's simply the reciprocal of tangent. First, we find that this is a 30-60-90 triangle. What is different is that it is in the second quartile, which means its x value is negative. Just put the x value on top of the y
and we get our answer:

But we're not through yet. Remember that we cannot have a fraction divided by a fraction. Negative square root of three and one are both being divided by two, we can cancel them out. This gives us our true answer

Peyton's Points: Here's some tips when doing problems with the unit circle.

1. Find out what kind of triangle you're being asked to solve.
2. Remember to think about which quartile it's in.
3. Remember that co secant, secant, and cotangent are all reciprocals of our basic sin, cosine, and tangent.
4. Rationalize your denominator if necessary.
5. Remember, you can't have fractions divided by fractions. See if you can cancel out the denominators of the fractions.

Woohoo! First post is in the books. If you need any more help, check out Mr. Corn's Website. Until next time, keep your pants off the ground, or you WILL be looking like a fool.

Peyton