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Chapter 6: Problem 9

Convert the point with the given polar coordinates to rectangular coordinates \((x, y) .\) polar coordinates \(\left(10, \frac{\pi}{6}\right)\)

Short Answer

Expert verified
The rectangular coordinates for the given polar coordinates \(\left(10, \frac{\pi}{6}\right)\) are \(\left(5\sqrt{3}, 5\right)\).

Step by step solution

01

Identify the polar coordinates

The given polar coordinates are (r, 胃) = (10, 蟺/6).
02

Convert r and 胃 to x and y using the conversion formulas

Use the conversion formulas for x and y: x = r * cos(胃) y = r * sin(胃) Plug in the given polar coordinates (10, 蟺/6): x = 10 * cos(蟺/6) y = 10 * sin(蟺/6)
03

Calculate x and y

Now, calculate the x and y coordinates: x = 10 * cos(蟺/6) = 10 * \(\frac{\sqrt{3}}{2}\) = 5\(\sqrt{3}\) y = 10 * sin(蟺/6) = 10 * \(\frac{1}{2}\) = 5
04

Write the rectangular coordinates as a pair (x,y)

The rectangular coordinates for the given polar coordinates are (x, y) = (5\(\sqrt{3}\), 5).

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Most popular questions from this chapter

Evaluate \(|4-3 i|\).

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