Find Amplitude, Period, and Phase Shift y=cos((6pix)/5+pi/3)

$y = \cos (\frac{6 π x}{5} + \frac{π}{3})$

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

$a = 1$

$b = \frac{6 π}{5}$

$c = - \frac{π}{3}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $1$

Find the period of $\cos (\frac{6 π x}{5} + \frac{π}{3})$ .

Tap for more steps...

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

$\frac{2 π}{| b |}$

Replace $b$ with $\frac{6 π}{5}$ in the formula for period.

$\frac{2 π}{| \frac{6 π}{5} |}$

$\frac{6 π}{5}$ is approximately $3.76991118$ which is positive so remove the absolute value

$\frac{2 π}{\frac{6 π}{5}}$

Multiply the numerator by the reciprocal of the denominator.

$2 π \frac{5}{6 π}$

Cancel the common factor of $2 π$ .

Tap for more steps...

Factor $2 π$ out of $6 π$ .

$2 π \frac{5}{2 π (3)}$

Cancel the common factor.

$2 π \frac{5}{2 π \cdot 3}$

Rewrite the expression.

$\frac{5}{3}$

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: $\frac{- \frac{π}{3}}{\frac{6 π}{5}}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $- \frac{π}{3} \cdot \frac{5}{6 π}$

Cancel the common factor of $π$ .

Tap for more steps...

Move the leading negative in $- \frac{π}{3}$ into the numerator.

Phase Shift: $\frac{- π}{3} \cdot \frac{5}{6 π}$

Factor $π$ out of $- π$ .

Phase Shift: $\frac{π \cdot - 1}{3} \cdot \frac{5}{6 π}$

Factor $π$ out of $6 π$ .

Phase Shift: $\frac{π \cdot - 1}{3} \cdot \frac{5}{π \cdot 6}$

Cancel the common factor.

Phase Shift: $\frac{π \cdot - 1}{3} \cdot \frac{5}{π \cdot 6}$

Rewrite the expression.

Phase Shift: $\frac{- 1}{3} \cdot \frac{5}{6}$

Multiply $\frac{- 1}{3}$ and $\frac{5}{6}$ .

Phase Shift: $\frac{- 1 \cdot 5}{3 \cdot 6}$

Simplify the expression.

Tap for more steps...

Multiply $- 1$ by $5$ .

Phase Shift: $\frac{- 5}{3 \cdot 6}$

Multiply $3$ by $6$ .

Phase Shift: $\frac{- 5}{18}$

Move the negative in front of the fraction.

Phase Shift: $- \frac{5}{18}$

List the properties of the trigonometric function.

Amplitude: $1$

Period: $\frac{5}{3}$

Phase Shift: $- \frac{5}{18}$ ( $\frac{5}{18}$ to the left)

Vertical Shift: None

Do you know how to Find Amplitude, Period, and Phase Shift y=cos((6pix)/5+pi/3)? 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	three hundred thirty-eight million nine hundred sixty-six thousand six hundred twenty-eight

Interesting facts

338966628 has 64 divisors, whose sum is 938710080
The reverse of 338966628 is 826669833
Previous prime number is 13

Basic properties

Is Prime? no
Number parity even
Number length 9
Sum of Digits 51
Digital Root 6

Name

Name	one billion six hundred thirty-seven million six hundred eighty thousand six hundred forty-six

Interesting facts

1637680646 has 32 divisors, whose sum is 3210170880
The reverse of 1637680646 is 6460867361
Previous prime number is 5659

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	one billion seven hundred eighty-three million one hundred ninety-one thousand one hundred sixty-two

Interesting facts

1783191162 has 16 divisors, whose sum is 3624848352
The reverse of 1783191162 is 2611913871
Previous prime number is 61

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 39
Digital Root 3

Find the Exact Value tan((-14pi)/4)

Find the Exact Value cos(3/4*pi)

Solve the Triangle a=100 , b=120 , c=85

Evaluate seventh root of 600

Graph y=2cos(x+pi/3)