Sine is a periodic function, which means that it repeats itself after completing a certain distance horizontally. In the case of y = sin x, the period is 2 times pi, measured in radians rather than degrees as is standard when dealing with trigonometric functions. Adding or subtracting from the input value x before the sine operation is performed results in a horizontal shift without changing the period. This is also referred to as a phase shift. The function cosine is identical to a sine function shifted left by pi / 2, so the two functions are sometimes used interchangeably.
Instructions
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1
Find the x value of the first peak of the sine wave right of the vertical axis.
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2
Subtract pi / 2 from the horizontal value at the first peak. The result may be negative. For example, a sine wave with a first peak at 3pi / 2 becomes 2pi / 2 after subtraction, which becomes simply pi.
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3
Change the sign of the value found after subtraction. Write this value, with its positive or negative sign, in the blank in the equation -- y = sin(x ____ ). For example, a sine wave with a first peak at 3pi / 2 would result in y = sin(x - pi).