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Exercises Trigonometry

Example 3 from Algebra and Trigonometry, 10.3 Polar Coordinates

Writing Polar Coordinates as Rectangular Coordinates

Write the polar coordinates $(3, \frac{π}{2})$ 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
Use the equivalent relationships.

$\begin{array}{l} x = r \cos θ \\ x = 3 \cos \frac{π}{2} = 0 \\ y = r \sin θ \\ y = 3 \sin \frac{π}{2} = 3 \end{array}$
The rectangular coordinates are $(0, 3) .$ See Figure 6.

Figure 6

How did it go?

PreviousPlotting a Point in the Polar Coordinate System with a Negative Component Next Writing Polar Coordinates as Rectangular 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.