Find Amplitude, Period, and Phase Shift -2cos(x/4-pi/3)+2

$- 2 \cos (\frac{x}{4} - \frac{π}{3}) + 2$

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

$a = - 2$

$b = \frac{1}{4}$

$c = \frac{π}{3}$

$d = 2$

Find the amplitude $| a |$ .

Amplitude: $2$

Find the period using the formula $\frac{2 π}{| b |}$ .

Find the period of $- 2 \cos (\frac{x}{4} - \frac{π}{3})$ .

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{4}$ in the formula for period.

$\frac{2 π}{| \frac{1}{4} |}$

$\frac{1}{4}$ is approximately $0.25$ which is positive so remove the absolute value

$\frac{2 π}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \cdot 4$

Multiply $4$ by $2$ .

$8 π$

Find the period of $2$ .

The period of the function can be calculated using $\frac{2 π}{| b |}$ .

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{1}{4}$ in the formula for period.

$\frac{2 π}{| \frac{1}{4} |}$

$\frac{1}{4}$ is approximately $0.25$ which is positive so remove the absolute value

$\frac{2 π}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \cdot 4$

Multiply $4$ by $2$ .

$8 π$

The period of addition/subtraction of trig functions is the maximum of the individual periods.

$8 π$

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

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: $\frac{\frac{π}{3}}{\frac{1}{4}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $\frac{π}{3} \cdot 4$

Combine $\frac{π}{3}$ and $4$ .

Phase Shift: $\frac{π \cdot 4}{3}$

Move $4$ to the left of $π$ .

Phase Shift: $\frac{4 π}{3}$

List the properties of the trigonometric function.

Amplitude: $2$

Period: $8 π$

Phase Shift: $\frac{4 π}{3}$ ( $\frac{4 π}{3}$ to the right)

Vertical Shift: $2$

Find Amplitude, Period, and Phase Shift -2cos(x/4-pi/3)+2

Related Questions

Support LCMGCF.com by disabling your adblocker.