Harmonic Form in Trigonometry

This investigation explores the shapes of graphs of the form y = acos x + bsin x as a and b take different values and link the resulting graph to the scale factor of the stretch of a basic trigonometric graph. The matching activity introduces y = Rcos(x + a) and y = Rsin(x + a). It has six graphs which must be matched to two forms of their equation. Subsequent tasks explore finding R and a from the graph as decimal values establishing the need for an algebraic method to find exact values of R and a. The resources are in first given in degrees and repeated in radians.