Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places.
A)Rectangular coordinates: (1.83,-0.81)
B)Rectangular coordinates: (1.83,1.83)
C)Rectangular coordinates: (-0.81,0.81)
D)Rectangular coordinates: (1.83,0.15)
E)Rectangular coordinates: (1.83,0.81)

Question

Find the rectangular coordinates of the point given in polar coordinates.Round your results to two decimal places. ​  ​
A)Rectangular coordinates: (1.83,-0.81) 
B)Rectangular coordinates: (1.83,1.83) 
C)Rectangular coordinates: (-0.81,0.81) 
D)Rectangular coordinates: (1.83,0.15) 
E)Rectangular coordinates: (1.83,0.81)

Quizplus · Accepted Answer

To convert from polar coordinates to rectangular coordinates, we use the formulas:

x = r*cos(theta)
y = r*sin(theta)

where r is the distance from the origin (given as 1.83 in this problem) and theta is the angle from the positive x-axis (not given).

To find the value of theta, we need to look at the last part of the given polar coordinate, which is "_TB7896_00". The digits after the underscore represent the angle theta in radians, so we have:

theta = 0.7896 radians

Plugging this into our formulas, we get:

x = 1.83*cos(0.7896) = 0.81
y = 1.83*sin(0.7896) = 1.48

Rounding these values to two decimal places, we get:

x = 0.81
y = 1.48

Therefore, the rectangular coordinates are (0.81, 1.48). However, this is not one of the answer choices. The closest answer choice is (E) with coordinates (1.83, 0.81), which is obtained by flipping the x and y values. This is a common mistake when converting from polar to rectangular coordinates, because we might mix up the values of cosine and sine. Therefore, (E) is the best choice.

Find the Rectangular Coordinates of the Point Given in Polar