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Chapter 6: Problem 38

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$\left(-6, \frac{3 \pi}{2}\right)$$

Short Answer

Expert verified
The rectangular coordinates of the point \((-6, 3 \pi/2)\) in polar coordinates are \((0, 6)\) in Cartesian coordinates.

Step by step solution

01

Apply the formula to find 'x' coordinate

The 'x' coordinate is found using the equation \( x = r \cos(\theta) \). Substitute \( r = -6 \) and \( \theta = 3 \pi / 2 \) into the formula. Hence, the x-coordinate is \( x = -6 \cdot cos(3 \pi / 2) \).
02

Solve for 'x' coordinate

\(\cos(3 \pi / 2) = 0 \). So, \( x = -6 \cdot 0 = 0 \).
03

Apply the formula to find 'y' coordinate

The 'y' coordinate is found using the equation \( y = r \sin(\theta) \). Substitute \( r = -6 \) and \( \theta = 3 \pi / 2 \) into the formula. Hence, the y-coordinate is \( y = -6 \cdot sin(3 \pi / 2) \).
04

Solve for 'y' coordinate

\(\sin(3 \pi / 2) = -1 \). So, \( y = -6 \cdot -1 = 6 \).
05

Write down the rectangular coordinates

Having computed both coordinates, the rectangular coordinates of the given point are (0, 6).

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Most popular questions from this chapter

Exercises \(81-83\) will help you prepare for the material covered in the next section. Two airplanes leave an airport at the same time on different runways. The first plane, flying on a bearing of \(\mathrm{N} 66^{\circ} \mathrm{W},\) travels 650 miles after two hours. The second plane, flying on a bearing of \(\mathrm{S} 26^{\circ} \mathrm{W},\) travels 600 miles after two hours. Illustrate the situation with an oblique triangle that shows how far apart the airplanes will be after two hours.

Solve the equation \(2 x^{3}+5 x^{2}-4 x-3=0\) given that -3 is a zero of \(f(x)=2 x^{3}+5 x^{2}-4 x-3\) (Section \(2.4,\) Example 6 )

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Will help you prepare for the material covered in the next section. Simplify: \(4(5 x+4 y)-2(6 x-9 y)\)
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