00:01
This problem, we want to write the six primary trig ratios in terms of line segments.
00:05
So in the original red triangle here that's given, we can deal with two of those already.
00:13
We see that sine theta is equal to ap over hypotenuse 1.
00:21
So sine theta is ap.
00:24
We also see that coast theta is adjacent.
00:29
That's oa over hypotenuse 1, and that means cost theta is equal to oa.
00:39
Now we're going to focus on a different triangle.
00:41
So if this angle is theta, that means this is a 90 minus theta.
00:47
And if this is 90 minus theta, we also know that this one is 90 minus theta because of some of our parallel line rules, which means the last angle up top here is also theta.
01:01
Because a tangent against the circle creates a 90 degree angle.
01:07
So i'm going to focus on this purple triangle on the top left now.
01:13
And in the purple triangle, we can see that sine theta is equal to opposite over hypotenuse...