Find Amplitude, Period, and Phase Shift y=sin((6x)/7+1/6)

$y = \sin (\frac{6 x}{7} + \frac{1}{6})$

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

$a = 1$

$b = \frac{6}{7}$

$c = - \frac{1}{6}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $1$

Find the period of $\sin (\frac{6 x}{7} + \frac{1}{6})$ .

Tap for more steps...

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{6}{7}$ in the formula for period.

$\frac{2 π}{| \frac{6}{7} |}$

$\frac{6}{7}$ is approximately $0.\overline{857142}$ which is positive so remove the absolute value

$\frac{2 π}{\frac{6}{7}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \frac{7}{6}$

Cancel the common factor of $2$ .

Tap for more steps...

Factor $2$ out of $2 π$ .

$2 (π) \frac{7}{6}$

Factor $2$ out of $6$ .

$2 (π) \frac{7}{2 (3)}$

Cancel the common factor.

$2 π \frac{7}{2 \cdot 3}$

Rewrite the expression.

$π \frac{7}{3}$

Combine $π$ and $\frac{7}{3}$ .

$\frac{π \cdot 7}{3}$

Move $7$ to the left of $π$ .

$\frac{7 π}{3}$

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

Tap for more steps...

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: $\frac{- \frac{1}{6}}{\frac{6}{7}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $- \frac{1}{6} \cdot \frac{7}{6}$

Multiply $- \frac{1}{6} \cdot \frac{7}{6}$ .

Tap for more steps...

Multiply $\frac{7}{6}$ and $\frac{1}{6}$ .

Phase Shift: $- \frac{7}{6 \cdot 6}$

Multiply $6$ by $6$ .

Phase Shift: $- \frac{7}{36}$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $\frac{7 π}{3}$

Phase Shift: $- \frac{7}{36}$ ( $\frac{7}{36}$ to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=sin((6x)/7+1/6)? If not, you can write to our math experts in our application. The best solution for your task you can find above on this page.

Name

Name	nine hundred ninety-four million eight hundred forty-four thousand three hundred eighty

Interesting facts

994844380 has 32 divisors, whose sum is 2686854240
The reverse of 994844380 is 083448499
Previous prime number is 8461

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 49
Digital Root 4

Name

Name	one hundred ninety million seven hundred sixty-one thousand seven hundred forty-one

Interesting facts

190761741 has 8 divisors, whose sum is 213834360
The reverse of 190761741 is 147167091
Previous prime number is 113

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 36
Digital Root 9

Name

Name	three hundred eighty-one million sixty-seven thousand two hundred eighty-four

Interesting facts

381067284 has 128 divisors, whose sum is 1358477568
The reverse of 381067284 is 482760183
Previous prime number is 13

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 39
Digital Root 3

Evaluate square root of 11( square root of 6- square root of 5)

Graph y=3/4x-7/2

Graph y=3sin(pix+pi/2)

Find Amplitude, Period, and Phase Shift f(x)=tan(x/2)

Find the Exact Value cos((7pi)/4-(11pi)/6)