00:01
This problem lets us to use the xy coordinates in the given figure to find the value of the trig function at the indicated real number t or state that the expression is undefined.
00:09
And the trig evaluation we're supposed to find is co -siecon of 5 pi over 3.
00:13
And the first thing we need to do is figure out the xy points at 5 pi over 3, which on our unit circle, which we see portions of in our diagram here, 5 pi over 3 would be attached to the xy point of 1ā2 negative square root 3 over 2.
00:30
So if that's our angle that we're trying to evaluate at, we can then focus on what we need, either the x value, the y value, or y over x or x over y, depending on what trick function we're looking at.
00:42
And when we're looking at cosecant, co -sequent is the reciprocal of sign.
00:46
So if we can find one over sine of 5 pi over 3, then we can evaluate to figure out what co -seekin of 5 pi over 3 is.
00:56
And sine at an angle wants the y value at that.
01:00
Given angle.
01:01
So when we look at 5 pi over 3 on our diagram, the y value at 5 pi over 3 is negative square root 3 over 2.
01:07
So our evaluation, co -sieken of 5 pi over 3, will be equivalent to 1 divided by the y value at 5 5 5 or 3, which is negative square root 3 over 2...