TrigonometricFunctionsof Anglesin StandardPosition
Above,we definedthe six trigonometricfunctionsfor anglesin right triangles.We can also definethe same
functionsin termsof anglesof rotation.Consideran anglein standardposition,whoseterminalside intersects
a circleof radiusr. We can thinkof the radiusas the hypotenuseof a right triangle:
The point(x, y) wherethe terminalside of the angleintersectsthe circletells us the lengthsof the two legs
of the triangle.Now, we can definethe trigonometricfunctionsin termsofx, y,andr:
Now we can extendthesefunctionsto includenon-acuteangles.
Example4:The point(-3, 4) is a pointon the terminalside of an anglein standardposition.Determinethe
valuesof the six trigonometricfunctionsof the angle.
Solution:
Noticethat the angleis morethan 90 degrees,and that the terminalside of the anglelies in the second
quadrant.This will influencethe signsof the trigonometricfunctions.