00:01
You're told that the tangent of theta is four thirds and theta's in the third quadrant.
00:04
We also know that the sine of phi is negative root 10 over 10, and we know that phi is in the fourth quadrant.
00:10
So we're being asked to find the sign of theta minus phi.
00:13
Well, this is our difference formula.
00:15
So remember, the formula for this is that it'll be sine of theta times the cosine of five minus the cosine of theta times the sine of phi.
00:28
So we need to know the sign and cosine values for these formulas.
00:32
Well, let's start with theta.
00:34
We're told the tangent of theta.
00:36
Well, remember, we also are told the quadrant that it's in.
00:39
So let's actually start by drawing this out.
00:42
So if it's in the third quadrant, we'll draw this down here, and then this would be our theta.
00:48
So because the tangent is four thirds, remember, that's opposite over adjacent.
00:52
So the opposite would be four, the adjacent would be three.
00:55
And actually, they would both be negative because we're in the third quadrant.
00:58
Well, this is one of our special right triangles.
01:00
This is a 3 -4 -5 triangle, so we know the hypotenuse is 5.
01:04
So now we can find the sine and cosine values for this angle.
01:08
The sign is opposite over hypotenuse, so the sine of theta would be negative 4 fifths.
01:14
And the cosine of theta is the adjacent over hypotenuse, so it would be negative 3 fifths.
01:19
Perfect.
01:19
Now we have a sine and cosine for theta.
01:22
Well, now we need the same for 5.
01:24
Well, we know the sign, we just don't know the cosine.
01:27
So we need to draw this up.
01:29
But again, we know that phi is in the fourth quadrant.
01:32
So we can draw our angle in the fourth quadrant...