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Students explore vertical and phase shifts of sine and cosine functions.
Students utilize the Transformation Graphing application to investigate the amplitude of trigonometric functions.
The program will graph the parent function y = sin(x) and define Y1 = a sin(x) into the screen. Students can enter different values for a and observe the effect on the function. They should find that the sine curve is vertically stretched by a factor of |a|.
Next, students investigate the period of a trigonometric graph.
Here, Y1 = sin(bx), and students substitute given values for b, observing the effects on the function. They will find that the value of b affects the horizontal stretch of this function and thus changes the period.
Students investigate a simple phase shift. The program will graph Y1 = sin(x + c) and students substitute given values of c to observe the shift.
Students then investigate a vertical shift. Investigating as before, students will find that the equation Y1 = sin(x) + d has a vertical shift equal to the parameter d.
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