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Chapter 6: Problem 40

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$(8.3,4.6)$$

Short Answer

Expert verified
The rectangular coordinates of the point would be calculated using the above steps. Please ensure to use radians for angle calculation.

Step by step solution

01

Understand Conversion Formulas

The formulas to convert polar coordinates to rectangular coordinates are given by: \(x = r \cdot cos(\theta)\) and \(y = r \cdot sin(\theta)\). Here, \(x\) and \(y\) are the rectangular coordinates while \(r\) is the distance from the origin and \(\theta\) is the angle.
02

Substituting Values

Substitute \(r = 8.3\) and \(\theta= 4.6\) into the conversion formulas. This will give: \(x = 8.3 \cdot cos(4.6)\) and \(y = 8.3 \cdot sin(4.6)\).
03

Calculate Rectangular Coordinates

After calculating \(x\) and \(y\), one gets the corresponding rectangular coordinates. Please note that angle \(\theta\) is usually measured in radians for these calculations.

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