The angle <math><mstyle displaystyle="true"><mfrac><mrow><mn>2</mn><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac></mstyle></math> is an angle where the values of the six trigonometric functions are known. Because this is the case, add <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> to keep the value the same.

Use the sum formula for cosine to simplify the expression. The formula states that <math><mstyle displaystyle="true"><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>+</mo><mi>B</mi><mo>)</mo></mrow><mo>=</mo><mo>-</mo><mrow><mo>(</mo><mi>cos</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>cos</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>+</mo><mi>sin</mi><mrow><mo>(</mo><mi>A</mi><mo>)</mo></mrow><mi>sin</mi><mrow><mo>(</mo><mi>B</mi><mo>)</mo></mrow><mo>)</mo></mrow></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> .

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><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

The exact value of <math><mstyle displaystyle="true"><mi>sin</mi><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mn>0</mn></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>sin</mi><mrow><mo>(</mo><mfrac><mrow><mi>π</mi></mrow><mrow><mn>3</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> is <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> by <math><mstyle displaystyle="true"><mfrac><mrow><msqrt><mn>3</mn></msqrt></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> .

Add <math><mstyle displaystyle="true"><mo>-</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> and <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> .

Do you know how to Expand Using Sum/Difference Formulas cos((2pi)/3)? 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 two hundred fourteen million fifteen thousand five hundred fifty-nine |
---|

- 1214015559 has 4 divisors, whose sum is
**1618687416** - The reverse of 1214015559 is
**9555104121** - Previous prime number is
**3**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 33
- Digital Root 6

Name | one billion seven hundred eighty-four million three hundred eleven thousand three hundred twenty-three |
---|

- 1784311323 has 8 divisors, whose sum is
**2386832448** - The reverse of 1784311323 is
**3231134871** - Previous prime number is
**307**

- Is Prime? no
- Number parity odd
- Number length 10
- Sum of Digits 33
- Digital Root 6

Name | eight hundred forty-three million three hundred forty-eight thousand two hundred twenty-four |
---|

- 843348224 has 1024 divisors, whose sum is
**21918988800** - The reverse of 843348224 is
**422843348** - Previous prime number is
**71**

- Is Prime? no
- Number parity even
- Number length 9
- Sum of Digits 38
- Digital Root 2