First: Konigsburg
Next: Homework
when solving a situation, consider the context, if there is any.
if you want further discussion on the ambiguous case (when we have two sides and an angle that's not in between them), check out here.
i think it's the music that really sells it.
If you want problems to try that include the ambiguous case, check out these.
Then: Trigonometry as a function.
the goal of this section is to make sure you can create an equation that goes around in a circle.
This can be achieved with sine or cosine fairly easily, as long as we follow the pieces we did in class.
here is your moment of zen. Sine is the height as we go around the circle, and cosine is the distance away from the center. They are the same thing, time shifted ninety degrees.
here is a link to the desmos I made for it.
change each of the variables and make sure you understand what's happening to it.
Example Problem #1: https://www.desmos.com/calculator/eahsu7ulj6
Example Problem #2: https://www.desmos.com/calculator/gvagplqdtq
Finally: Trigonometry as Trigonometric Identities (it's quite possible we don't make it here today)
This should allow us to look at sin^2 + cos^2 = 1 .... and why that matters.
Let's combine some values and see what they look like in desmos. Try to quantify and possibly simplify some of these.
Looking at our sheet of information (from that super old book), let's see if we can add some facts we can use.