Answered: "Which of the following polar coordinate pairs does..."

Jaden Easton

Answered question

2021-09-06

Which of the following polar coordinate pairs does not represent the point with rectangular coordinates (-2,-2)?
(A)

(2 \sqrt{2} . - 135 °)

(B)

(2 \sqrt{2} . 225 °)

(C)

(- 2 \sqrt{2} . - 315 °)

(D)

(- 2 \sqrt{2} . 45 °)

(E)

(- 2 \sqrt{2} . 135 °)

Answer & Explanation

Nathanael Webber

Skilled2021-09-07Added 117 answers

A polar coordinate $(r; θ)$ is given, then $(x; y) = (r \times \cos θ; r \times \sin θ)$

A) $(2 \sqrt{2} \cos (- 135^{\circ}), 2 \sqrt{2} \sin (- 135^{\circ})) = (2 \sqrt{2} \times - \frac{\sqrt{2}}{2}; 2 \sqrt{2} \times - \frac{\sqrt{2}}{2}) = (- 2; - 2)$

B) $(2 \sqrt{2} \cos 225^{\circ}, 2 \sqrt{2} \sin 225^{\circ}) = (2 \sqrt{2} \times - \frac{\sqrt{2}}{2}; 2 \sqrt{2} \times - \frac{\sqrt{2}}{2}) = (- 2; - 2)$

C) $(- 2 \sqrt{2} \cos (- 315^{\circ}), - 2 \sqrt{2} \sin (- 315^{\circ})) = (- 2 \sqrt{2} \times \frac{\sqrt{2}}{2}; - 2 \sqrt{2} \times \frac{\sqrt{2}}{2}) = (- 2; - 2)$

D) $(- 2 \sqrt{2} \cos 45^{\circ}, - 2 \sqrt{2} \sin 45^{\circ}) = (- 2 \sqrt{2} \times \frac{\sqrt{2}}{2}; - 2 \sqrt{2} \times \frac{\sqrt{2}}{2}) = (- 2; - 2)$

E) $(- 2 \sqrt{2} \cos 135^{\circ}, - 2 \sqrt{2} \sin 135^{\circ}) = (- 2 \sqrt{2} \times - \frac{\sqrt{2}}{2}; - 2 \sqrt{2} \times \frac{\sqrt{2}}{2}) = (2; - 2)$

Choice (E) does not represent $(- 2; - 2)$ .

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Calculus 2

Didn't find what you were looking for?