Question

Which pair represents (4, –4) in polar plane?

A. (6.56, 47.77)
B. (6.56, 43.77)
C. (5.66, 44.76)
D. (5.56, 47.77)

Answer 1

Answer on Question # 34605 – Math – Trigonometry

Question: Which pair represents $(4, -4)$ in polar plane?

A. (6.56, 47.77)

B. (6.56, 43.77)

C. (5.66, 44.76)

D. (5.56, 47.77)

Solution

We use the following formulas:

$$x = r \cos \varphi$$ $$y = r \sin \varphi$$

where $(x, y)$ is defined in Cartesian coordinate system.

So, we have the system:

$$\left\{ \begin{array}{l} 4 = r \cos \varphi \\ -4 = r \sin \varphi \end{array} \right.$$ $$\text{Divide the second by the first one:}$$ $$\tan \varphi = -1 \Rightarrow \varphi = \frac{1}{4} (4\pi n - \pi), n \in \mathbb{Z}.$$ $$\text{So } r = \frac{4}{\cos \frac{\pi}{4}} = 4\sqrt{2} \approx 5.66$$

Answer: C. (5.66, 44.76)

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