Although you have not made it clear, your original coordinates are polar coordinates where the first coordinate represents a radius and and the second coordinate represents an angle. An angle of pi/2 is 90 degrees rotated anti-clockwise from the positive x axis. Your angle of 3pi/2 is an angle of 270 degrees anticlockwise from the positive x axis as can be seen in this diagram of the the unit circle.
If you look at the diagram you can see that the angle of 3pi/2 on the unit circle is also marked as (0,-1) in regular "Cartesian coordinates" which is a another name for rectangular coordinates where coordinates are expressed in terms of (x,y).
The unit circle has a radius of one, but your polar coordinate has a radius of 4 so you must multiply the radius part of the coordinate by 4 to obtain the final answer in rectangular coordinates of (0,-4).
Your question is fairly easy, but for more difficult angles you can directly convert polar coordinates to rectangular coordinates using the the formulas and methods shown here:
(4,3Pi/2) is like an arrow with its tail at the origin of the rectangular coordinate system with its head terminating 4 units along the negative y-axis. 270 degrees is measured from positive x-axis (0 deg reference) going counterclockwise terminating at the negative y-axis (90 degrees per quadrant). Therefore (4,3Pi/2) in polar coordinates is equivalent to ( 0, -4)
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Although you have not made it clear, your original coordinates are polar coordinates where the first coordinate represents a radius and and the second coordinate represents an angle. An angle of pi/2 is 90 degrees rotated anti-clockwise from the positive x axis. Your angle of 3pi/2 is an angle of 270 degrees anticlockwise from the positive x axis as can be seen in this diagram of the the unit circle.
http://en.wikipedia.org/wiki/Trigonometric_functio...
If you look at the diagram you can see that the angle of 3pi/2 on the unit circle is also marked as (0,-1) in regular "Cartesian coordinates" which is a another name for rectangular coordinates where coordinates are expressed in terms of (x,y).
The unit circle has a radius of one, but your polar coordinate has a radius of 4 so you must multiply the radius part of the coordinate by 4 to obtain the final answer in rectangular coordinates of (0,-4).
Your question is fairly easy, but for more difficult angles you can directly convert polar coordinates to rectangular coordinates using the the formulas and methods shown here:
http://en.wikipedia.org/wiki/Polar_coordinates#Con...
3Pi/2 is equal to 3(180)/ 2 = 270 degrees
(4,3Pi/2) is like an arrow with its tail at the origin of the rectangular coordinate system with its head terminating 4 units along the negative y-axis. 270 degrees is measured from positive x-axis (0 deg reference) going counterclockwise terminating at the negative y-axis (90 degrees per quadrant). Therefore (4,3Pi/2) in polar coordinates is equivalent to ( 0, -4)
4 /_ 3Ï/2 = 4 (cos 3Ï/2 + i sin 3Ï/2)
4 /_ 3Ï/2 = i 4sin 3Ï/2 = - 4 i
Coordinates are (0 , - 4)
Answer: (4 cos(3Ï/2), 4 sin(3Ï/2)) = (0, -4)
(4cos 3Ï/2, 4sin 3Ï/2) = (0, -4)
(0,-4)
(0, -4)