00:01
Okay, so for this question, given that sine of theta is equal to 12 over 13, we're asked for the remaining trig functions.
00:16
So, knowing this, we can actually construct a triangle here.
00:24
We're told that it's in quadrant 2.
00:26
That's why i drew a right triangle in quadrant 2.
00:29
And this is the angle we're looking at, theta.
00:32
Sine of theta is 12 over 13 that's opposite over the hypotenuse this means this is 12 and the hypotenuse here is 13 now to solve for the other side we can simply use the pythagorean theorem which is 13 squared minus 12 squared is equal to that other side which is let's name it c squared so this is 169 minus 144, that would give us 25.
01:09
And the square root of 25 is equal to 5.
01:15
But this angle goes out to the left.
01:19
That means this side is actually negative 5.
01:23
So now we can easily figure out the other trick functions...