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The Natural Cosine and Sine Curves
This mathlet illustrates the relationship between the graphs of the natural (radian measure) sine and cosine curves and the vertical and horizontal coordinates of points on the unit circle. It can be used in calculus classes to provide an alternative way of understanding the derivative rules for sine and cosine. (See the text frame for more details.)
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This applet is offered in the spirit of animating proofs without words. We hope to convey the meaning of the natural sine and cosine graphs and the symbolic formulas for their periodicity, phase shifts, rates of change can be understood dynamically, visually, in unison. It also serves as the basis for a unified rotational approach to the addition formulas, complex multiplication, and the geometric interpretation of the dot product. It might be most helpful in looking ahead to preview or looking back to review the connections among the different ways of viewing these seemingly diverse concepts.
Open The Natural Sine and Cosine Curves in a new window.
Published December, 2001
© 2001 by Bob Palais