/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 34 Polar coordinates of a point are... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Polar coordinates of a point are given. Find the rectangular coordinates of each point. $$\left(6,180^{\circ}\right)$$

Short Answer

Expert verified
The rectangular coordinates of the point are (-6, 0)

Step by step solution

01

Conversion of angle from degrees to radians

Initially, the angle θ is given in degrees. However, the trigonometric functions in the formulas for x and y require the angle to be in radians. The conversion from degrees to radians is performed by multiplying the angle in degrees by π/180. Therefore, θ = 180 degrees * π/180 = π radians.
02

Calculation of x-coordinate

The x-coordinate is calculated using the formula x = r cos θ. Substitute r = 6 and θ = π into the formula. Therefore, x = 6 cos π = -6
03

Calculation of y-coordinate

The y-coordinate is calculated using the formula y = r sin θ. Substitute r = 6 and θ = π into the formula. Therefore, y = 6 sin π = 0. However, the sine of π is zero, meaning that y = 0.

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