Q
QuestionMathematics

The Cartesian coordinates of a point are given. (a) (−6, 6) (i) Find polar coordinates (r, 𝜃) of the point, where r > 0 and 0 ≤ 𝜃 < 2𝜋. (ii) Find polar coordinates (r, 𝜃) of the point, where r < 0 and 0 ≤ 𝜃 < 2𝜋. (b) (4, 4) (i)Find polar coordinates (r, 𝜃) of the point, where r > 0 and 0 ≤ 𝜃 < 2𝜋. (ii) Find polar coordinates (r, 𝜃) of the point, where r < 0 and 0 ≤ 𝜃 < 2𝜋.
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Answer

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Step 1

So, the polar coordinates of the point are $(6\sqrt{2}, \frac{7\pi}{4})$.
Substituting these values into the formulas, we get:

Step 2

So, the polar coordinates of the point are $(-6\sqrt{2}, \frac{15\pi}{4})$.
In this case, we need to add $\pi$ to our value of $\theta$:

Final Answer

(a) (i) $(6\sqrt{2}, \frac{7\pi}{4})$ (a) (ii) $(- 6\sqrt{2}, \frac{15\pi}{4})$ (b) (i) $(4\sqrt{2}, \frac{\pi}{4})$ (b) (ii) $(- 4\sqrt{2}, \frac{5\pi}{4})$