Find the Exact Value csc((2pi)/3)

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Trigonometry

$\csc (\frac{2 π}{3})$

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

$\csc (\frac{π}{3})$

The exact value of $\csc (\frac{π}{3})$ is $\frac{2}{\sqrt{3}}$ .

$\frac{2}{\sqrt{3}}$

Multiply $\frac{2}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{2}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Combine and simplify the denominator.

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Multiply $\frac{2}{\sqrt{3}}$ and $\frac{\sqrt{3}}{\sqrt{3}}$ .

$\frac{2 \sqrt{3}}{\sqrt{3} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{2 \sqrt{3}}{{\sqrt{3}}^{1} \sqrt{3}}$

Raise $\sqrt{3}$ to the power of $1$ .

$\frac{2 \sqrt{3}}{{\sqrt{3}}^{1} {\sqrt{3}}^{1}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{2 \sqrt{3}}{{\sqrt{3}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 \sqrt{3}}{{\sqrt{3}}^{2}}$

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$\frac{2 \sqrt{3}}{{(3^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 \sqrt{3}}{3^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2 \sqrt{3}}{3^{\frac{2}{2}}}$

Divide $1$ by $1$ .

$\frac{2 \sqrt{3}}{3^{1}}$

Evaluate the exponent.

$\frac{2 \sqrt{3}}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{2 \sqrt{3}}{3}$

Decimal Form:

$1.15470053 \dots$

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Name

Name	one billion four hundred ninety-two million eight hundred twenty-seven thousand two hundred eighty-nine

Interesting facts

1492827289 has 8 divisors, whose sum is 1543627008
The reverse of 1492827289 is 9827282941
Previous prime number is 587

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 52
Digital Root 7

Name

Name	one billion seven hundred twenty-nine million six hundred sixty-five thousand two hundred sixty-three

Interesting facts

1729665263 has 4 divisors, whose sum is 1751559840
The reverse of 1729665263 is 3625669271
Previous prime number is 79

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 47
Digital Root 2

Name

Name	three hundred thirty million four hundred twenty-seven thousand nine hundred four

Interesting facts

330427904 has 1024 divisors, whose sum is 12702778344
The reverse of 330427904 is 409724033
Previous prime number is 2

Basic properties

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

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