Lesson Summary 22/8 - R Formula

Introduction: Graphical method

Graphs of 5sinθ + 2cosθ and sqrt(29)sin(θ+21.8º)

The graph of sqrt(29)sin(θ+21.8º) is an approximation, and thus is slightly out of phase with the graph of 5 sin θ + 2 cos θ. However, when drawn, the 2 graphs are almost the same, which reflects that the functions 5sinθ + 2cosθ and sqrt(29)sin(θ+21.8º) are identical.

Graph of 5sinθ and graph of 2cosθ

Finding Ymin and Ymax of the functions from the graph:

The Ymax and Ymin values of 5sinθ + 2cosθ and sqrt(29)sin(θ+21.8º) are not the Ymax and Ymin values of 5sinθ and 2cosθ added together.

Graph of 5sinθ + 2cosθ plotted with the graphs of 5sinθ and 2cosθ

Algebraic Method:

Solving 5sinθ + 2cosθ =0:

Solving 5sinθ + 2cosθ by expressing in the form Rsin(θ+α), to find the ymin and ymax:

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