On Friday, we checked over homework, then started on Day 2 of Unit Circle and Radians. You can find homework answers on moodle.
10-4 (Day 2) More Unit Circle and Radians.
Overall, we learned in this section how to:
1. convert between degree and radian, and between radian and degree
2. fill in our very first unit circle!!
First off, we defined what a radian actually is: the angle created by placing a radius along the circumference of a circle. (If this doesn't make sense, think of a slice of pizza cut in triangular shapes, from the inside out. Take the crust, and that is what the radian is.)
VERY IMPORTANT: for this chapter, and possibly beyond this, you need to switch your calculator mode. Here's how it's done:
1. press home then #5
2. choose #2 for settings
3. choose #1 for general
4. tab down until you reach Angle
5. choose Degree or Radian
6. tab down until you reach Make Default
7. press enter
8. select OK
If you forget to switch modes, you'll notice that you're not going to get your answers in either degree or radian mode.
If we know that 360 degrees around a circle gives us an arc length of 2π, then 180 degrees around will give us half of that..which is just π.
One fourth of that will gives us π divided by two so it's just π/2.
This information will help us convert between degree and radian, and radian and degree.
Think of it like this. What you want to get rid of it on the bottom, and what you want is on the top.
We then practiced converting some measures.
ex. Rad. to Deg.
and from Deg. to Rad.
1 deg. = 1xπ/180 = π/80 (if you're converting to radians, leave in simplest form, so leave the π in)
It's going to be a bit difficult to explain, but once it's actually filled out, the unit circle does make sense.
Let's start off with a 30-60-90 triangle.
The measures are shown, and the way we use this information is by finding
the cos and sin of some angles.
These answers will be later added to the unit circle.