00:01
Okay, so first step here, let's remember my quadrants.
00:02
My first quadrant, x and y are both positive, second, x negative, y is positive, third, x and y is positive, third, x and y are both negative, and then fourth.
00:11
Suppose i know that tangent of an angle x is 2 over 3, and this is in the third quadrant.
00:18
So if i draw a right triangle in the third quadrant with angle x with respect to the x axis, my tangent ratio, what's my ratio for tangent? well, one way to remember this is the acronym sokotoa.
00:32
Tangent is opposite over adjacent.
00:35
The side opposite of the angles to the adjacent angle.
00:39
So the adjacent side, side right next to it, that's attached to the leg, is going to be three.
00:46
Okay, so before i move forward, let's just find the missing side in my right triangle.
00:53
If i know two sides, how do i find the third side in a right triangle? well, to find sidelines, i'm used to pythagorean theorem, whereas sokatoa, the trig ratios have to do with the relationship between the angles and the sides.
01:07
So this will be one side squared plus the other side squared equals the hypotenuse, cross -man -9 -angle squared, 4 plus 9 equals c -squared or 13 equals c -squared.
01:18
Take the square root of both sides.
01:21
Square of 13 doesn't simplify, so i'm going to leave it as a square to 13.
01:26
Then i'm going to find some relationship, sign of 2x, how do i find sign of 2x? well, this is 2 times sine of x times cosine of x.
01:37
Now i don't know what sign of 2x is, but i know sine of x is just sine is opposite over hypotenuse in this triangle, opposite side, is 2.
01:46
Hypotenuse is square to 13.
01:49
Coside of x is adjacent over hypotenuse in the x triangle, so adjacent side 3 over hypotenuse square to 13 times 2.
01:59
Multiply my top numbers.
02:00
2 times 2 is 4 times 3...
