problemsin lesson7.)
The Sine,Cosine,and TangentFunctions
The first threetrigonometricfunctionswe will work with are the sine, cosine,and tangentfunctions.As noted
above,the elementsof the domainsof thesefunctionsare angles.We can definethesefunctionsin terms
of a right triangle:The elementsof the rangeof the functionsare particularratiosof sidesof triangles.
We definethe sine functionas follows:For an acuteanglexin a right triangle,is the sinxratio of the side
oppositeof the angleto the hypotenuseof the triangle.For example,in the triangleshownabove,we have:
Sinceall right triangleswith the sameacuteangleare similar, this functionis will producethe sameratio,
no matterwhichtriangleis used.Thus,it is a well definedfunction.
Similarly, the cosineof an angleis definedas the ratio of the side adjacent(nextto) the angleto the hy-
potenuseof the triangle.In the triangleabove,we have:
Finally, the tangentof an angleis definedas the ratio of the side oppositethe angleto the side adjacentto
the angle.In the triangleabove,we have:
Thereare a few importantthingsto note aboutthe way we writethesefunctions.First,keepin mindthat the
abbreviationssin(x),cos(x),andtan(x)are just likef(x). Theysimplifystandfor specifickindsof functions.