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Exercises Trigonometry

Example 4 from Algebra and Trigonometry, 10.3 Polar Coordinates

Writing Polar Coordinates as Rectangular Coordinates

Write the polar coordinates $(- 2, 0)$ as rectangular coordinates.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
See Figure 7. Writing the polar coordinates as rectangular, we have

$\begin{array}{l} x = r \cos θ \\ x = −2 \cos (0) = −2 \\ y = r \sin θ \\ y = −2 \sin (0) = 0 \end{array}$
The rectangular coordinates are also $(- 2, 0) .$

Figure 7

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write the polar coordinates $(- 1, \frac{2 π}{3})$ as rectangular coordinates.

How did it go?

PreviousWriting Polar Coordinates as Rectangular Coordinates Next Writing Rectangular Coordinates as Polar Coordinates

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.