"Convert to polar coordinates. (3, 3)" was answered by our experts

College
Calculus and Analysis
Integral Calculus
Parametric equations, polar coordinates, and vector-valued functions

emancipezN

Answered question

2021-01-17

Convert to polar coordinates. (3, 3)

Answer & Explanation

svartmaleJ

Skilled2021-01-18Added 92 answers

Given coordinate is (3, 3). We have to convert given coordinate into polar coordinate. In Polar form coordinate is given as $(r, θ)$ . We know that in polar coordinates, we have $t a n θ = \frac{y}{x} a n d r = \sqrt{x^{2} + y^{2}}$ Therefore, $\tan θ = \frac{3}{3}$ $\tan θ = 1$ $θ = \tan^{-} 1 (1) θ \frac{π}{4}$

Here $θ = \frac{π}{4}$ is in the first quadrant. So r will be positive. Therefore, $r = \sqrt{x^{2} + y^{2}}$ $= \sqrt{3^{2} + 3^{2}}$ $= \sqrt{9 + 9}$ $= \sqrt{18}$ $= 3 \sqrt{2}$ Therefore, $r = 3 \sqrt{2} a n d θ = \frac{π}{4}$ . Hence, polar coordinates will be $(3 \sqrt{2}, \frac{π}{4})$ .

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