Find Amplitude, Period, and Phase Shift y=1/2cos(3x+pi/2)

$y = \frac{1}{2} \cos (3 x + \frac{π}{2})$

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

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

$b = 3$

$c = - \frac{π}{2}$

$d = 0$

Find the amplitude $| a |$ .

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

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

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

$\frac{2 π}{| b |}$

Replace $b$ with $3$ in the formula for period.

$\frac{2 π}{| 3 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$\frac{2 π}{3}$

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: $\frac{- \frac{π}{2}}{3}$

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: $- \frac{π}{2} \cdot \frac{1}{3}$

Multiply $- \frac{π}{2} \cdot \frac{1}{3}$ .

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Multiply $\frac{1}{3}$ and $\frac{π}{2}$ .

Phase Shift: $- \frac{π}{3 \cdot 2}$

Multiply $3$ by $2$ .

Phase Shift: $- \frac{π}{6}$

List the properties of the trigonometric function.

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

Period: $\frac{2 π}{3}$

Phase Shift: $- \frac{π}{6}$ ( $\frac{π}{6}$ to the left)

Vertical Shift: None

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Name

Name	one hundred twelve million five hundred sixteen thousand five hundred forty-seven

Interesting facts

112516547 has 8 divisors, whose sum is 132187440
The reverse of 112516547 is 745615211
Previous prime number is 13

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 32
Digital Root 5

Name

Name	one billion four hundred thirty-four million six hundred thirty-six thousand seven hundred twenty-four

Interesting facts

1434636724 has 64 divisors, whose sum is 3542745600
The reverse of 1434636724 is 4276364341
Previous prime number is 31

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 40
Digital Root 4

Name

Name	one billion five hundred seventy-eight million seven hundred forty-four thousand three hundred eighty-one

Interesting facts

1578744381 has 8 divisors, whose sum is 2106107424
The reverse of 1578744381 is 1834478751
Previous prime number is 1901

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 48
Digital Root 3

Find the Exact Value cos(0.75)

Graph y=tan(x)+2

Solve for x 50=25sin((2pi)/7t)+75

Factor by Grouping sin(x)tan(x)

Verify the Identity 1/(cos(x)-sin(x))=cos(x)+sin(x)