1) y=3sin(2x) and y=3cos(2x) 2) y=4sin(2x-pi) and y=cos(3x-pi/2)

Question

compare and contrast all

1. the amplitudes
2. periods of the two factors
3. y-minimums and y-maximums
4. phase shifts

complete sentences

Answer 1

With these formats:

y=a•sin(b(x-c)) + d

y=a•cos(b(x-c)) + d

Where:

|a| = amplitude

2π/b = period

c = phase shift

d = vertical shift

d-a and d+a are the y-minimum and y-maximum

*Based on their respective parent functions.

(1) y=3•sin(2x) and y=3•cos(2x) 

Amplitudes are the same and both equal to 3.

Periods are the same and they are both equal to π.

y-min and y-max are also the same (both equal to -1 and 1)

Zero phase shift on both.

*The only difference on these two when you graph it is the sine function is odd and symmetric about the origin while the cosine function is even and symmetric about the y-axis.

(2)y=4•sin(2x-π) and y=cos(3x-π/2)

y=4•sin(2x-π)

y=4•sin(2(x-π/2))

(a) Amplitude = 4

(b) Period = 2π/2 = π

(c) y-min and y-max = -4 and 4

(d) phase shift is π/2 to the right

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y=cos(3x-π/2)

y=cos(3(x-π/6))

(a) Amplitude = 1

(b) Period = (2/3)π

(c) y-min and y-max are -1 and 1

(d) Phase shift is π/6 to the right.