Find Amplitude, Period, and Phase Shift f(x)=1/7cot(8theta-120)

$f (x) = \frac{1}{7} \cot (8 θ - 120)$

The function declaration $f (x)$ varies according to $x$ , but the input function $\frac{1}{7} \cdot \cot (8 θ - 120)$ only contains the variable $θ$ . Assume $f (θ) = \frac{1}{7} \cdot \cot (8 θ - 120)$ .

$f (θ) = \frac{1}{7} \cdot \cot (8 θ - 120)$

Use the form $a \cot (b θ - c) + d$ to find the variables used to find the amplitude, period, phase shift, and vertical shift.

$a = \frac{1}{7}$

$b = 8$

$c = 120$

$d = 0$

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

Amplitude: None

Find the period of $\frac{\cot (8 θ - 120)}{7}$ .

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The period of the function can be calculated using $\frac{π}{| b |}$ .

$\frac{π}{| b |}$

Replace $b$ with $8$ in the formula for period.

$\frac{π}{| 8 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $8$ is $8$ .

$\frac{π}{8}$

Find the phase shift using the formula $\frac{c}{b}$ .

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The phase shift of the function can be calculated from $\frac{c}{b}$ .

Phase Shift: $\frac{c}{b}$

Replace the values of $c$ and $b$ in the equation for phase shift.

Phase Shift: $\frac{120}{8}$

Divide $120$ by $8$ .

Phase Shift: $15$

List the properties of the trigonometric function.

Amplitude: None

Period: $\frac{π}{8}$

Phase Shift: $15$ ( $15$ to the right)

Vertical Shift: None

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