Question

Convert the rectangular coordinates (4√3,−4) to polar form. Let r>0 and 0≤θ<2π.

Enter your answer by filling in the boxes. Enter coordinates as simplified fractions or radicals in simplest form.

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Answer 1

Answer:

(8,150)

Step-by-step explanation:

Polar form is in,

(r,theta).

To find r, apply pythagorean theorem using both coordinates to find r.

$(4 \sqrt{3} ) {}^{2} + ( - 4 {}^{2} ) = {r}^{2}$

$48 + 16 = {r}^{2}$

$r = 8$

To find theta, since we know the opposite and adjacent side, apply the tangent function.

$\tan(x) = \frac{ - 4}{4 \sqrt{3} }$

Apply inverse tan function

$\tan {}^{ - 1} ( \frac{ - 4}{4 \sqrt{3} } ) = - 30$

Since the degrees have to be in between 0 and 360. Add 180 to -30.

$- 30 + 180 = 150$

So the answer is

(8,150).