Take the inverse cosine of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>t</mi></mstyle></math> from inside the cosine.

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

The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the reference angle from <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> to find the solution in the fourth quadrant.

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

Write each expression with a common denominator of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> , by multiplying each by an appropriate factor of <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Combine.

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

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"><mn>1</mn></mstyle></math> in the formula for period.

Solve the equation.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

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

The period of the <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>2</mn><mi>π</mi></mstyle></math> radians in both directions.

Consolidate the answers.

Do you know how to Solve for x cos(t)=0? 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 | four hundred thirty-four million one hundred twenty-five thousand one hundred forty-three |
---|

- 434125143 has 16 divisors, whose sum is
**643472640** - The reverse of 434125143 is
**341521434** - Previous prime number is
**4643**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 27
- Digital Root 9

Name | two billion ninety-four million nine hundred eighty-two thousand two hundred fifty-two |
---|

- 2094982252 has 64 divisors, whose sum is
**5207864544** - The reverse of 2094982252 is
**2522894902** - Previous prime number is
**1753**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 43
- Digital Root 7

Name | two billion one hundred forty-four million four hundred thirty-two thousand five hundred thirteen |
---|

- 2144432513 has 8 divisors, whose sum is
**2272684032** - The reverse of 2144432513 is
**3152344412** - Previous prime number is
**1087**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 29
- Digital Root 2