Find the Exact Value cot(240)

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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	seven hundred sixteen million nine hundred eighty-seven thousand nine hundred ninety-one

Interesting facts

716987991 has 8 divisors, whose sum is 965449584
The reverse of 716987991 is 199789617
Previous prime number is 101

Basic properties

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

Name

Name	one billion five hundred fifty-six million seventy-nine thousand one hundred twenty-nine

Interesting facts

1556079129 has 8 divisors, whose sum is 1621664000
The reverse of 1556079129 is 9219706551
Previous prime number is 33

Basic properties

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

Name

Name	one billion one hundred thirty million eight hundred eighty-seven thousand four hundred twelve

Interesting facts

1130887412 has 32 divisors, whose sum is 2565222912
The reverse of 1130887412 is 2147880311
Previous prime number is 293

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 35
Digital Root 8

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