determine the sine of 135 degrees the cosine of 135 degrees and teh tangent of 135 degrees so lets start off just by drawing a 135 degree angle in standard position so to do that let me draw some axis and i'll put a unit circle on that axis that's about as good as i can hand draw the unit circle and let me mark this up i'll mark it up a little bit neater so this is when x is equal to one and this is when y is equal to one. this is when y is equal to negitive no excuse me this is when x is equal to negative onw and this is when y is equal to negitive one and the only reason why i had to draw kind of a dotted line is that i find it easier to draw a dotted line we can fill it in and it actually should be a filled in line so there you go now lets draw a 135 degree angle in standard position so lets sit the vertex of that angle at the origin, let me do this in a new color so this is going to sit at the origin the initial side is going to go along the positive x-axis just like that draw it as a ray. and then the terminal side since it's a positive 135 degrees we're going to go in a counterclockwise direction if we go straight up to the y axis that gives us 90 degrees we have to get to 135 so we have to go another 45 so we have to go another 45 it takes us about right about half way or exactly half way through the second quadrant so it takes us right over there. so that is 135 degree angle now we know from our the unit circle definition of trig function that the intersection between the terminal side and the unit circle is going to have some coordinates (x,y) we know from the unit circle definition that x is equal to the cosine of 135 degrees in this case and y is going to equal the sine of 135 degrees and we know that y over x is going to be equal to the tangent of 135 degrees so if we can figure out this intersection point the x and y coordinates we've essintially figured out this entire problem. and there is a little bit of a hint, what i'm going to do is create a triangle here and this really does show the connection that show's that the unit circle definition is really just an extention of the traditional soh cah toa right trainagle definition so what i'm going to do is drop, i'm gonna do is create a right triangle