28Chapter 1•Right Triangle Trigonometry§1.4Example1.23xy00◦(1,0)90◦(0,1)180◦(−1,0)270◦(0,−1)Figure 1.4.6Find the exact values of all six trigonometric functions of 0◦, 90◦,180◦, and 270◦.Solution:These angles are different from the angles we have con-sidered so far, in that the terminal sides lie along either thex-axisor they-axis. So unlike the previous examples, we do not have anyright triangles to draw.However, the values of the trigonometricfunctions are easy to calculate by picking the simplest points on theirterminal sides and then using the definitions in formulas (1.2) and(1.3).For instance, for the angle 0◦use the point (1,0) on its terminalside (the positivex-axis), as in Figure 1.4.6. You could think of theline segment from the origin to the point (1,0) as sort of a degenerateright triangle whose height is 0 and whose hypotenuse and base havethe same length 1. Regardless, in the formulas we would user=1,x=1, andy=0. Hence:sin 0◦=yr=01=0cos 0◦=xr=11=1tan 0
This is the end of the preview.
access the rest of the document.