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#34745 – 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 formula:

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

where $(x, y)$ – a Cartesian coordinate system.

So, we have the system: $\begin{cases} 4 = r \cos \varphi \\ -4 = r \sin \varphi \end{cases}$. Divide the second on the first:

$$\tan \varphi = -1 \rightarrow \varphi = \frac{1}{4} (4\pi n - \pi), n \in \mathbb{Z}$$

So, $r = \frac{4}{\cos \pi} = 4\sqrt{2} = 5.66$.

Answer. C