00:01
Problem, they tell you that the tangent of theta is equal to negative three forms.
00:04
And we also know that theta is in the second, is in the fourth quadrant.
00:08
So what we want to do is find sign of theta over two, meaning we need to use our half angle formula.
00:14
Well, the first thing is, well, what is our half angle formula for sign? well, remember, the formula is plus or minus the square root of one minus the cosine of theta divided by two.
00:26
So in this case, we're not given the cosine of theta.
00:29
So we have to go ahead and find it.
00:30
Well, remember, tangent of theta, theta is in the fourth quadrant.
00:35
So if we would draw our angle, we would have an angle down here in the fourth quadrant.
00:39
So here would be my angle for theta.
00:41
Remember, tangent is opposite over adjacent.
00:44
So that means my opposite would be negative three, and my adjacent would be four.
00:49
So now we have to find cosine.
00:51
When order to find cosine, we need the hypotenuse.
00:54
Now, if you recognize, this is one of our special pythagorean triples, 3, 4 ,5, you know that your hypotenuse is 5.
01:01
If you didn't recognize that, you could use pythagrin theorem, and you'd still find that your hypotenuse is 5.
01:07
So now we can find the cosine of this angle.
01:10
Remember, cosine is equal to the adjacent side over the hypotenuse.
01:14
So the cosine of theta would equal to four -fifths.
01:19
So now let's substitute this into our expression.
01:21
So we'll have the sign of theta over 2 equals plus or minus, the square root of 1 minus, or remember the cosine of theta was 4 -5.
01:30
So have 1 minus 4 fifths all over 2...