00:01
In this problem, our ultimate goal is to find the sign of a plus b.
00:03
Well, we know the sign of a is one -third, the cosine of b is three -fifths, and we know that a and b are between 0 and pi over 2.
00:11
Well, first off, we have a sum formula for the sign of a plus b.
00:14
It says that the sign of angle a times the cosine of angle b is equal, or plus the cosine of angle a times the sine of angle b.
00:25
So we do know the sign of angle a and the cosine of angle b, but we need our cosine and sine values.
00:30
So in order to do this, we're going to draw their reference triangles.
00:33
Now, because a and b are between 0 and pi over 2, that means they're both located in the first quadrant.
00:39
So i'm going to go ahead and draw angle a.
00:41
Well, we know the sign value is equal to 1 3 3.
00:44
Remember, that's the ratio of the opposite over the hypotenuse.
00:48
So what we can do is solve for the adjacent side by using the pythagorean theorem.
00:52
So we'll have x squared plus 1 squared equal to 3 squared, 1 squared is equal to 1, 3 squared, 3 squared, the 9, so we'll subtract 1 from both sides, so have x squared equal to 8, and now we'll take the square of both sides, so x will equal the square of the v.
01:08
So now we'll go back in our picture, and i'll label that adjacent side to square of the v.
01:13
Now, similarly, what we're going to do is we're going to draw angle b.
01:16
So again, we know it's in the first quadrant, but this time we know the cosine.
01:20
That is the ratio of the adjacent side over the hypotenuse.
01:24
So this time we need to find the opposite side.
01:27
But again, we're going to use pythagorean theorem.
01:29
So have y squared plus three squared equals five squared...