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sashaice [31]
1 year ago
9

I need help with this practice problem It is from my ACT prep guide It asks to graph the function, if you can, use Desmos to com

plete

Mathematics
1 answer:
Vaselesa [24]1 year ago
6 0

Given the following function:

\text{ f(x) = cot(x + }\frac{\pi}{6})

Use the form a·cot(bx - c) to find the variables used to find the amplitude, period, phase shift and vertical shift.

We get,

a = 1

b = 1

c = -π/6

d = 0

Since the graph of the Cotangent function does not have a maximum or minimum value, there can be no value for the amplitude.

Amplitude: None

For the Period:

\text{ Period = }\frac{\text{ }\pi}{\text{ b}}\text{ = }\frac{\pi}{1}\text{ = }\pi

Therefore, the Period is π.

For the Phase Shift:

\text{ Phase Shift = }\frac{\text{ c}}{\text{ b}}\text{ = }\frac{-\frac{\pi}{6}}{1}\text{ = -}\frac{\pi}{6}

Therefore, Phase Shift is -π/6 → π/6 (To the left).

For the Vertical Shift:

Vertical Shift = 0

Plotting the function will be:

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I'll use text forms of the logical symbols because copying/pasting on mobile is annoying.

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(b) To rewrite XOR, first distribute the NOT over the AND using DeMorgan's law:

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p XOR q = (p AND NOT q) OR (q AND NOT p)

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p IFF q = (p OR NOT q) AND (q OR NOT p)

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NOT (p IFF q) = NOT ((p OR NOT q) AND (q OR NOT p))

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The statements in bold match, so p XOR q is indeed equivalent to NOT (p IFF q).

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