Find the Exact Value cot(240 degrees )

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Trigonometry

$\cot (240 °)$

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

$\cot (60)$

The exact value of $\cot (60)$ is $\frac{1}{\sqrt{3}}$ .

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

Multiply $\frac{1}{\sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

Combine and simplify the denominator.

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Multiply $\frac{1}{\sqrt{3}}$ and $\frac{\sqrt{3}}{\sqrt{3}}$ .

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

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

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

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Divide $1$ by $1$ .

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

Evaluate the exponent.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.57735026 \dots$

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Name

Name	six hundred eighty-seven million five hundred ninety-one thousand eight hundred sixty-one

Interesting facts

687591861 has 8 divisors, whose sum is 1000133664
The reverse of 687591861 is 168195786
Previous prime number is 11

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 51
Digital Root 6

Name

Name	two billion one hundred thirty-one million six hundred fifty-seven thousand eight hundred sixty-eight

Interesting facts

2131657868 has 16 divisors, whose sum is 4850121240
The reverse of 2131657868 is 8687561312
Previous prime number is 89

Basic properties

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

Name

Name	one billion four hundred seventy-four million eight hundred thirty-three thousand three hundred seventy-five

Interesting facts

1474833375 has 32 divisors, whose sum is 3272166144
The reverse of 1474833375 is 5733384741
Previous prime number is 5

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 45
Digital Root 9

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