Find Amplitude, Period, and Phase Shift y=-1/2*cos(pix-pi/18)

$y = - \frac{1}{2} \cdot \cos (π x - \frac{π}{18})$

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

$a = - \frac{1}{2}$

$b = π$

$c = \frac{π}{18}$

$d = 0$

Find the amplitude $| a |$ .

Amplitude: $\frac{1}{2}$

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

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

Period: $\frac{2 π}{| b |}$

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

Period: $\frac{2 π}{| π |}$

Solve the equation.

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$π$ is approximately $3.14159265$ which is positive so remove the absolute value

Period: $\frac{2 π}{π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

Period: $\frac{2 π}{π}$

Divide $2$ by $1$ .

Period: $2$

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: $\frac{\frac{π}{18}}{π}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $\frac{π}{18} \cdot \frac{1}{π}$

Cancel the common factor of $π$ .

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Cancel the common factor.

Phase Shift: $\frac{π}{18} \cdot \frac{1}{π}$

Rewrite the expression.

Phase Shift: $\frac{1}{18}$

Find the vertical shift $d$ .

Vertical Shift: $0$

List the properties of the trigonometric function.

Amplitude: $\frac{1}{2}$

Period: $2$

Phase Shift: $\frac{1}{18}$ ( $\frac{1}{18}$ to the right)

Vertical Shift: $0$

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Name

Name	one billion four hundred eighty-two million seven hundred fifty-one thousand one hundred forty-eight

Interesting facts

1482751148 has 8 divisors, whose sum is 3336190092
The reverse of 1482751148 is 8411572841
Previous prime number is 2

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 41
Digital Root 5

Name

Name	eight hundred four million two hundred seventy thousand nine hundred forty-two

Interesting facts

804270942 has 32 divisors, whose sum is 2147534208
The reverse of 804270942 is 249072408
Previous prime number is 773

Basic properties

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

Name

Name	three hundred twenty-six million two hundred fifty-four thousand four hundred forty-six

Interesting facts

326254446 has 64 divisors, whose sum is 689420160
The reverse of 326254446 is 644452623
Previous prime number is 7

Basic properties

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

Factor sin(x+y)-sin(x-y)

Find the Supplement pi/7

Solve for ? x=arcsin(-( square root of 2)/2)

Find the Inverse (x^2)/8+(3x^2)/2+(9x)/2

Convert to Trigonometric Form -8i