00:01
Okay, so suppose i know that tangent of an angle is 4 pi over 3.
00:05
And i know that the angle is between pi and 3 pi over 2.
00:08
So thinking about my standard form, 0 pi over 2, pi, 3 pi over 2, and then 2 pi, i know that i'm going to be in the third quadrant between pi and 3 pi over 2.
00:21
So i can draw a right triangle, t.
00:29
Okay, so i know that tangent is 1 over 1, opposite over adjacent.
00:33
The opposite side is 4, adjacent side of adjacent leg is 3.
00:38
And since i'm in the third quadrant, they're both negative.
00:42
Now to solve for my hypotenuse, i could do the pythagorean theorem, or i know that the sub -pythagorean triple 3, 4, 5, and the hypotenuse is always positive.
00:52
Okay, so now let's find my other values.
00:56
What's sine? well, sine is opposite over hypotenuse.
01:01
What's opposite of t? 4, negative 4, and hypotenuse is 5...