Convert to Rectangular Coordinates (4 square root of 3,pi/3)

Convert to Rectangular Coordinates (4 square root of 3,pi/3)

$(4 \sqrt{3}, \frac{π}{3})$

Use the conversion formulas to convert from polar coordinates to rectangular coordinates.

$x = r c o s θ$

$y = r s i n θ$

Substitute in the known values of $r = 4 \sqrt{3}$ and $θ = \frac{π}{3}$ into the formulas.

$x = (4 \sqrt{3}) \cos (\frac{π}{3})$

$y = (4 \sqrt{3}) \sin (\frac{π}{3})$

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$x = 4 \sqrt{3} (\frac{1}{2})$

$y = (4 \sqrt{3}) \sin (\frac{π}{3})$

Cancel the common factor of $2$ .

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Factor $2$ out of $4 \sqrt{3}$ .

$x = 2 (2 \sqrt{3}) (\frac{1}{2})$

$y = (4 \sqrt{3}) \sin (\frac{π}{3})$

Cancel the common factor.

$x = 2 (2 \sqrt{3}) (\frac{1}{2})$

$y = (4 \sqrt{3}) \sin (\frac{π}{3})$

Rewrite the expression.

$x = 2 \sqrt{3}$

$y = (4 \sqrt{3}) \sin (\frac{π}{3})$

$x = 2 \sqrt{3}$

$y = (4 \sqrt{3}) \sin (\frac{π}{3})$

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

$x = 2 \sqrt{3}$

$y = 4 \sqrt{3} (\frac{\sqrt{3}}{2})$

Cancel the common factor of $2$ .

Tap for more steps...

Factor $2$ out of $4 \sqrt{3}$ .

$x = 2 \sqrt{3}$

$y = 2 (2 \sqrt{3}) (\frac{\sqrt{3}}{2})$

Cancel the common factor.

$x = 2 \sqrt{3}$

$y = 2 (2 \sqrt{3}) (\frac{\sqrt{3}}{2})$

Rewrite the expression.

$x = 2 \sqrt{3}$

$y = 2 \sqrt{3} \sqrt{3}$

$x = 2 \sqrt{3}$

$y = 2 \sqrt{3} \sqrt{3}$

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

$x = 2 \sqrt{3}$

$y = 2 (\sqrt{3} \sqrt{3})$

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

$x = 2 \sqrt{3}$

$y = 2 {\sqrt{3}}^{1 + 1}$

Add $1$ and $1$ .

$x = 2 \sqrt{3}$

$y = 2 {\sqrt{3}}^{2}$

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

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Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x = 2 \sqrt{3}$

$y = 2 {(3^{\frac{1}{2}})}^{2}$

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

$x = 2 \sqrt{3}$

$y = 2 \cdot 3^{\frac{1}{2} \cdot 2}$

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

$x = 2 \sqrt{3}$

$y = 2 \cdot 3^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Tap for more steps...

Cancel the common factor.

$x = 2 \sqrt{3}$

$y = 2 \cdot 3^{\frac{2}{2}}$

Rewrite the expression.

$x = 2 \sqrt{3}$

$y = 2 \cdot 3$

$x = 2 \sqrt{3}$

$y = 2 \cdot 3$

Evaluate the exponent.

$x = 2 \sqrt{3}$

$y = 2 \cdot 3$

$x = 2 \sqrt{3}$

$y = 2 \cdot 3$

Multiply $2$ by $3$ .

$x = 2 \sqrt{3}$

$y = 6$

The rectangular representation of the polar point $(4 \sqrt{3}, \frac{π}{3})$ is $(2 \sqrt{3}, 6)$ .

$(2 \sqrt{3}, 6)$

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Name

Name	five hundred fifteen million seven hundred sixty-one thousand four hundred thirty-one

Interesting facts

515761431 has 4 divisors, whose sum is 687681912
The reverse of 515761431 is 134167515
Previous prime number is 3

Basic properties

Is Prime? no
Number parity odd
Number length 9
Sum of Digits 33
Digital Root 6

Name

Name	two billion forty-two million six hundred seventy-four thousand eight hundred fifty-four

Interesting facts

2042674854 has 16 divisors, whose sum is 4456745280
The reverse of 2042674854 is 4584762402
Previous prime number is 3

Basic properties

Is Prime? no
Number parity even
Number length 10
Sum of Digits 42
Digital Root 6

Name

Name	one billion six hundred forty-five million nine hundred thirty-eight thousand five hundred forty-three

Interesting facts

1645938543 has 16 divisors, whose sum is 2272859136
The reverse of 1645938543 is 3458395461
Previous prime number is 47

Basic properties

Is Prime? no
Number parity odd
Number length 10
Sum of Digits 48
Digital Root 3

Solve for x 16x+3=9x+2

Simplify cos(pi/2-x)

Evaluate cos((5pi)/8)

Graph y=cot(4x-pi/2)-3

Simplify arctan(( square root of 3)/1)

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$