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Chapter 6: Problem 39

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$(7.4,2.5)$$

Short Answer

Expert verified
The rectangular coordinates of the given point are approximately (-1.410, 6.969).

Step by step solution

01

Identify the given polar coordinates

The given polar coordinates are (7.4, 2.5). Here, the radial distance \(r = 7.4\) units and the angular position \(\theta = 2.5\) radians.
02

Apply the conversion formula for x-coordinate

The x-coordinate of the rectangular system is found using the formula \(x = r \cdot \cos(\theta)\). Substituting the known values gives \(x = 7.4 \cdot \cos(2.5)\).
03

Calculate the x-coordinate

Calculate the value of x by performing the multiplication and taking the cosine of 2.5. The calculated x-coordinate is approximately -1.410.
04

Apply the conversion formula for y-coordinate

The y-coordinate of the rectangular system is found using the formula \(y = r \cdot \sin(\theta)\). Substituting the known values gives \(y = 7.4 \cdot \sin(2.5)\).
05

Calculate the y-coordinate

Calculate the value of y by performing the multiplication and taking the sine of 2.5. The calculated y-coordinate is approximately 6.969.

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