Finding values for trig functions with the angles 0 90 180 and 360

finding the value of trig functions at the angle zero PI over 2 pi 3 PI over 2 and 2 pi so if you didn't watch the video on the unit circle stop right now and go back and watch it what I'm going to point out here is that this is exactly the same there is no difference the thing that thing the thing that seems confusing here is that when you go to the angle PI over 2 there's no triangle formed remember how we're using reference angles but the process is still exactly the same so here's what mean when you say sine of say PI over 2 we know that PI that the sine is over and the unit circle is always 1 so all do is go to PI over 2 and go to the point 4 PI over 2 and grab the by value which is 1 and see that the sine of PI over 2 is 1 the cosine of PI over 2 cosine is over and the unit circle is 1 and at PI over 2 we go look at the ordered pair and we see that is 0 so the cosine of PI over 2 is 0 over 1 which is 0 now if do the tangent of PI over 2 and the unit circle tangent is over and if look at the ordered pair the value is 1 and the value is 0 and we can't divide by 0 that means that the tangent of PI over 2 is undefined and remember when we do wall map undefined as DNE does not exist so whatever point grab if it's 3 PI over 2 or pi all do is look at the ordered pairs and grab the wire or grab the remember that is 1 in the unit circle and write out the Rachele and simplify let's take an example with the cosecant secant and cotangent functions let's do the cosecant of 0 radians or 0 degrees we know that cosecant is the reciprocal of sine and sine is over so the cosecant is over and the unit circle is 1 and if you go to the ordered pair and grab the uh-oh we're dividing by 0 this is undefined if said the secant of zero sequence reciprocal of cosine so it's over again r's wrong if we look at it's 1 and 1 over 1 is 1 the cotangent of 0 cotangent is over the reciprocal of tangent and if we look at the ordered pair the is 1 and the is 0 so the cotangent of 0 is undefined again how about down here let's do the will go sine cosine again let's do the sine of pi the sine of Pi its over and if look at the ordered pair at pi is 0 and ours one so it's zero the cosine of pi cosine is over and is negative one at that point is one and so we get negative one and how about the tangent of PI radians tangent is over is 0 is negative one so the tangent of pi is zero so it's just matter of looking at the ordered pair remembering what the ratios are remembering that is one making ratio and simplifying