The Pythagorean Theorem - Educational Outreach

Figure 3.17 can be used as a jumping-off point foran alternate method for simultaneously developing additionformulas for cos( ) and sin( ) . In Figure 3.18,the point {cos( ),sin( )} is decomposed intocomponents.y{cos( ),sin( )}x2 sin( )sin( )sin( )cos( )y2 sin( ) cos( ){cos( ),sin()}y1 sin( ) cos( )( 0,0) (1,0 )x1 cos( )cos( )xFigure 3.18: An Intricate TrigonometricDecompositionThis is done by using the fundamental definitions of sin( )and cos( ) based on both general right triangles and righttriangles having a hypotenuse of unit length as shown inFigure 3.16. The reader is asked to fill in the details on howthe various side-lengths in Figure 3.18 are obtained—agreat practice exercise for facilitating understanding ofelementary trigonometric concepts.125