Chapter 14, Problem 3CT

To determine

To find:The missing term.

Answer to Problem 3CT

The missing term are calculated.

Explanation of Solution

Given:

  

Calculation:

Calculate the rectangular coordinates for (3,120).

  $\begin{array}{c}x=3\cos 120\\ =-\frac{3}{2}\\ y=3\sin 120\\ =\frac{3\sqrt{3}}{2}\end{array}$

Calculate the rectangular coordinates for (-6,135).

  $\begin{array}{c}x=6\cos 135\\ =3\sqrt{2}\\ y=3\sin 135\\ =-3\sqrt{2}\end{array}$

Calculate the polar coordinates for (0,-4).

  $\begin{array}{c}r=\pm \sqrt{x^2+y^2}\\ =\pm 4\\ \sin \theta =\frac{y}{r}\\ \theta =270\end{array}$

Calculate the polar coordinates for ( $-\sqrt{5},\sqrt{5}$ ).

  $\begin{array}{c}r=\pm \sqrt{{\left(-\sqrt{5}\right)}^2+{\sqrt{5}}^2}\\ =\sqrt{10}\\ \sin \theta =\frac{y}{r}\\ \theta =135\end{array}$

Thus, the missing term are calculated.