Step 1 We want to find the exact value of sin From the text the quadrants are numbered counter clockwise from the upper right I II III IV This angle lies in quadrant III III K T sin 27 Step 2 Sketching the angle we draw the triangle formed with the terminal side and the x axis Looking at this triangle we see triangle that it is a 71 632 2 2 To find that value we first have to draw the angle 3 y Likewise the opposite side should be labeled 2A 3 From the text we know that the side lengths are 1 2 3 To label the sides with the proper lengths we note that 2 being the longest side length must be the hypotenuse The smallest angle will be opposite the shortest side Looking at the triangle and taking into account the quadrant so that the sign is correct the adjacent side should be labeled 3 x