Let <math><mstyle displaystyle="true"><mi>u</mi><mo>=</mo><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> . Substitute <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> for all occurrences of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>-</mo><mi>u</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> out of <math><mstyle displaystyle="true"><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mo>-</mo><mi>u</mi></mstyle></math> .

Factor <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> out of <math><mstyle displaystyle="true"><mi>u</mi><mo>⋅</mo><mi>u</mi><mo>+</mo><mi>u</mi><mo>⋅</mo><mo>-</mo><mn>1</mn></mstyle></math> .

Replace all occurrences of <math><mstyle displaystyle="true"><mi>u</mi></mstyle></math> with <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

If any individual factor on the left side of the equation is equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> , the entire expression will be equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Set <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

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

Simplify the right side.

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"><mn>90</mn></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>360</mn></mstyle></math> to find the solution in the fourth quadrant.

Subtract <math><mstyle displaystyle="true"><mn>90</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>360</mn></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.

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>360</mn></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>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> degrees in both directions.

Set <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn></mstyle></math> equal to <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Solve <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>=</mo><mn>0</mn></mstyle></math> for <math><mstyle displaystyle="true"><mi>θ</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> to both sides of the equation.

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

Simplify the right side.

The exact value of <math><mstyle displaystyle="true"><mi>arccos</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></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>360</mn></mstyle></math> to find the solution in the fourth quadrant.

Subtract <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> .

Find the period of <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mn>360</mn></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.

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>360</mn></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>θ</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mn>360</mn></mstyle></math> degrees in both directions.

The final solution is all the values that make <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>cos</mi><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mo>=</mo><mn>0</mn></mstyle></math> true.

Consolidate <math><mstyle displaystyle="true"><mn>90</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>270</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>90</mn><mo>+</mo><mn>180</mn><mi>n</mi></mstyle></math> .

Consolidate <math><mstyle displaystyle="true"><mn>360</mn><mi>n</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>360</mn><mo>+</mo><mn>360</mn><mi>n</mi></mstyle></math> to <math><mstyle displaystyle="true"><mn>360</mn><mi>n</mi></mstyle></math> .

Do you know how to Solve for θ in Degrees cos(theta)^2-cos(theta)=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 | six hundred eleven million nine hundred seventy-one thousand nine hundred sixty-four |
---|

- 611971964 has 16 divisors, whose sum is
**1377235656** - The reverse of 611971964 is
**469179116** - Previous prime number is
**27661**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 44
- Digital Root 8

Name | nine hundred seventy-seven million six hundred twenty-nine thousand two hundred eighty-seven |
---|

- 977629287 has 16 divisors, whose sum is
**1373567360** - The reverse of 977629287 is
**782926779** - Previous prime number is
**17203**

- Is Prime? no
- Number parity odd
- Number length 9
- Sum of Digits 57
- Digital Root 3

Name | one billion nine hundred twenty-eight million three hundred seventy thousand three hundred twelve |
---|

- 1928370312 has 128 divisors, whose sum is
**7199860608** - The reverse of 1928370312 is
**2130738291** - Previous prime number is
**113**

- Is Prime? no
- Number parity even
- Number length 10
- Sum of Digits 36
- Digital Root 9