Law of sines and cosines (for real this time). Both of them have links in class 12, so look there.
Application of the Law of sines and cosines.
Discussion on why there is an ambiguous case, without going too far down the rabbit hole.
if you want further discussion on the ambiguous case, 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.
Trigonometric movement.
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.
we then talked about sin^2 + cos^2 = 1.
this is another application of the Pythagorean Theorem, just written in a different form
it is used for Trigonometric Identities, which I'm going to guess we did not get to today. If we did, there will be more things below.
Homework:
do the questions assigned below. Extra denotes a higher level of difficulty and not required.
Law of Sines, page 435: 45, 47, 49. Extra is 48, 52 (consider where right angles might be)
Law of Cosines, page 442: 43, 44, 46, 51.
Extra is page 444: 60, 61, 62. for these you will need Heron's Formula, which is both findable and useable.
My question. This focuses on the Trigonometric movement. If you get stuck there are places online to help you, but don't jump there first. They may be using radians as well, so it may help you less than you think.
You are get into a ferris wheel, and are the last person to enter. The ferris wheel is three feet above the ground, completes a circle every 40 seconds, and has a diameter of 30 feet.
create an equation. You may want to use the desmos thing I made to help you. Link is above
For how long in each rotation are you above 45 feet?
The ferris wheel stops after 4 minutes. where am I on the ferris wheel?
Extra: How fast is the ferris wheel going?