00:01
In your question, you're to use the sum identity for the sine function to solve the following question.
00:06
So sine of a plus b is the question you're being asked to do.
00:10
The identity formula would be sine of the first angle times cosine of the second angle plus cosine of the first angle times sine of the second angle.
00:29
Now what you've been given to work with here is you've been given the value of cosine of a equaling 5 13ths and you've also been given the value, i'm sorry, the quadrant, that that's in quadrant four.
00:46
You've also been given the value of cosine of b equaling negative 15 17ths and you were told that that's in quadrant two.
00:58
All right, the approach that you want to use to these types of questions would be to sketch the angle in the appropriate quadrant, drawing a right triangle.
01:07
So we have this quadrant four angle.
01:12
So the angle that we're worried about here, this is your, your a.
01:18
Technically that doesn't mean much for you, but we create this triangle, this right triangle.
01:24
Cosine is the adjacent side over the hypotenuse in that right triangle.
01:29
So it would be five in the adjacent position, 13 in the hypotenuse position.
01:34
You would then want to figure out this missing side.
01:39
We'll call it y using the pythagorean theorem.
01:44
So it's five squared plus y squared equals 13 squared.
01:49
That's going to be 25 plus y squared equals 169.
01:55
Then subtract 25.
01:58
You'll get y squared equals 144.
02:01
Take the square root and you'll have y equals 12.
02:06
But in the position that that y is in, that would be a negative value.
02:11
So we want to consider that a negative 12.
02:14
Now that we have the triangle, you can determine the sign of a value as well because sign is the opposite side over the hypotenuse making sign of a negative 12 13ths.
02:32
So let's go ahead and do the same thing here for angle b.
02:38
Angle b is in quadrant two.
02:41
So it's like this.
02:44
It would create a right triangle.
02:47
And this time your adjacent side and hypotenuse are given.
02:52
The adjacent is negative 15...