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Chapter 6: Problem 98

Polar coordinates of a point are given. Use a graphing utility to find the rectangular coordinates of each point to three decimal places. $$(5.2,1.7)$$

Short Answer

Expert verified
The rectangular coordinates are approximately (1.944, 5.044).

Step by step solution

01

Understanding Conversion

Before proceeding, the nature of conversion from polar coordinates to rectangular needs to be clear. In polar coordinates, each point is represented by the radius and an angle, denoted as (r, 胃). To convert these into rectangular coordinates, the following formulae will be used: \(x = r \cdot cos(胃)\) and \(y = r \cdot sin(胃)\) where x and y are the rectangular coordinates we want to find, r is the given radius, and 胃 is the given angle in radians. In this problem, we are given r=5.2 and 胃=1.7.
02

Calculating X-coordinate

Let's begin by calculating the x-coordinate. Substitute r=5.2 and 胃=1.7 into the formula for x. \(x = 5.2 \cdot cos(1.7)\). Calculating this with the help of a calculator gives approximately \(x = 1.944\).
03

Calculating Y-coordinate

Now for the y-coordinate, substitute r=5.2 and 胃=1.7 into the formula for y. \(y = 5.2 \cdot sin(1.7)\). Using a calculator gives approximately \(y = 5.044\).

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