Use the form <math><mstyle displaystyle="true"><mi>a</mi><mi>cos</mi><mrow><mo>(</mo><mi>b</mi><mi>x</mi><mo>-</mo><mi>c</mi><mo>)</mo></mrow><mo>+</mo><mi>d</mi></mstyle></math> to find the variables used to find the amplitude, period, phase shift, and vertical shift.

Find the amplitude <math><mstyle displaystyle="true"><mrow><mo>|</mo><mi>a</mi><mo>|</mo></mrow></mstyle></math> .

Amplitude: <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math>

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> in the formula for period.

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The phase shift of the function can be calculated from <math><mstyle displaystyle="true"><mfrac><mrow><mi>c</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math> .

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>c</mi></mrow><mrow><mi>b</mi></mrow></mfrac></mstyle></math>

Replace the values of <math><mstyle displaystyle="true"><mi>c</mi></mstyle></math> and <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> in the equation for phase shift.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

Multiply the numerator by the reciprocal of the denominator.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>π</mi></mrow></mfrac></mstyle></math>

Cancel the common factor of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Cancel the common factor.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose></mrow><mrow><mn>2</mn></mrow></mfrac><mo>⋅</mo><mfrac><mrow><mn>1</mn></mrow><mrow><menclose notation="updiagonalstrike"><mi>π</mi></menclose></mrow></mfrac></mstyle></math>

Rewrite the expression.

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math>

Find the vertical shift <math><mstyle displaystyle="true"><mi>d</mi></mstyle></math> .

Vertical Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

List the properties of the trigonometric function.

Amplitude: <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math>

Period: <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Find the point at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> in the expression.

Simplify the result.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

Find the point at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>1</mn></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the expression.

Simplify the result.

Multiply <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

To write <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Find the point at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> in the expression.

Simplify the result.

Simplify each term.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Simplify terms.

Combine the numerators over the common denominator.

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>3</mn><mi>π</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mo>-</mo><mn>10</mn></mstyle></math> .

Find the point at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mn>2</mn></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> in the expression.

Simplify the result.

Move <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

To write <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> as a fraction with a common denominator, multiply by <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine fractions.

Combine <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn><mi>π</mi></mstyle></math> .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Find the point at <math><mstyle displaystyle="true"><mi>x</mi><mo>=</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Replace the variable <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> with <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> in the expression.

Simplify the result.

Simplify each term.

Combine <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> and <math><mstyle displaystyle="true"><mfrac><mrow><mn>5</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Move <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> to the left of <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> .

Simplify terms.

Combine the numerators over the common denominator.

Subtract <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>5</mn><mi>π</mi></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>4</mn><mi>π</mi></mstyle></math> .

Cancel the common factors.

Factor <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> out of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Divide <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Subtract full rotations of <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> until the angle is greater than or equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and less than <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The final answer is <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> .

List the points in a table.

The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.

Amplitude: <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math>

Period: <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math>

Phase Shift: <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> (<math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to the right)

Vertical Shift: <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math>

Do you know how to Graph y=10cos(pix-pi/2)? 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 | one billion six hundred sixty-three million nine hundred twenty-two thousand one hundred four |
---|

- 1663922104 has 32 divisors, whose sum is
**6047717256** - The reverse of 1663922104 is
**4012293661** - Previous prime number is
**13**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 34
- Digital Root 7

Name | six hundred thirty-three million three hundred forty-eight thousand seven hundred twenty-one |
---|

- 633348721 has 4 divisors, whose sum is
**650466292** - The reverse of 633348721 is
**127843336** - Previous prime number is
**37**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 37
- Digital Root 1

Name | nine hundred forty-three million eight hundred sixty-nine thousand seven hundred forty-nine |
---|

- 943869749 has 8 divisors, whose sum is
**950625720** - The reverse of 943869749 is
**947968349** - Previous prime number is
**197**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 59
- Digital Root 5