Today's soundtrack is Nagelfar: Hünengrab im Herbst, which is coincidentally the second black metal album that the Randomizer has issued me in as many days.
After taking a hiatus from math for several days, I'm back to continue the lesson on Angles in Standard Position that I started on the ninth.
When dealing with angles in standard position that have a terminal point, there are three things that we will be asked to find:
1) The distance from the origin to the terminal point (r)
2) The trigonometric ratios of the angle, which we call "theta," symbolized "θ"
3) The measure of θ in degrees
How to find the distance from the origin to the terminal point
So to find the distance from the origin to the terminal point, we can just use the Pythagorean Theorem. This will be easy enough to find, as we are using a graph, and we know the x- and y-coordinates. We know that a² + b² = c², when c is the hypotenuse. Now, we will always know our a² and b² - they are simply the x- and y-coordinates of the terminal point. So if we take x² + y², we will get c², the square root of which is the length of our hypotenuse!
How to find the trigonometric ratios of an angle
After we find the length of the hypotenuse, we will have the lengths of all sides of our triangle. At this point, we can find the three trigonometric ratios: sin θ (opposite over hypotenuse), cos θ (adjacent over hypotenuse), and tan θ (opposite over adjacent).
How to find the measure of θ in degrees
Once we know any trigonometric ratio of θ, we can find its angles in degrees by calculating, for example, tan⁻¹(1.5), which gives us 56.3°.