Philip P. answered • 05/17/14

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1) y=tan(2x)

a) The tangent function does not have an amplitude since its range is ±∞

b) The tangent's range is ±∞, so it has no maximum or minimum

c) The 2 in the argument of the tangent cuts the period in half. The period of tan(x) is pi, so the period of tan(2x) is pi/2.

2) y=3sin(x/3)

a) The amplitude of sin(x) is 1. The amplitude of 3 sin(x) is 3

b) The range of 3sin(x/3) is ±3, so +3 is its maximum and -3 is its minimum.

c) the period of sin(x) is 2pi. The 1/3 in the argument makes the sine function take 3 times longer to complete its period, so the period of 3sin(x/3) = (2pi)(3) = 6pi