1)Find the polar coordinates of the point whose rectangular coordinates are (4, -4).
2)Find the polar coordinates of the point whose rectangular coordinates are (-3,-3).
3)Find the rectangular coordinates of the point whose polar coordinates are (-4, ð/6)
4)Find the rectangular coordinates of the point whose polar coordinates are (2, 3ð/4).6).
5)Find the rectangular coordinates of the point whose polar coordinates are (6, ð/3)
We don't do homework for students, however, we can offer advice, critiques, and help. What is it you do not know about changing coordinate systems?
http://www.teacherschoice.com.au/Maths_Library/Coordinates/polar_-_rectangular_conversion.htm
We don't do homework for students, however, we can offer advice, critiques, and help. What is it you do not know about changing coordinate systems?
http://www.teacherschoice.com.au/Maths_Library/Coordinates/polar_-_rectangular_conversion.htm
To find the polar coordinates of a point given its rectangular coordinates, you can use the following formulas:
1) Polar coordinate r = sqrt(x^2 + y^2), where x and y are the given rectangular coordinates.
Polar coordinate theta (in radians) = arctan(y/x)
2) For negative coordinates, r remains the same and theta (in radians) is adjusted accordingly:
Polar coordinate theta = arctan(y/x) + pi
To find the rectangular coordinates of a point given its polar coordinates, you can use the following formulas:
3) Rectangular coordinate x = r * cos(theta), where r and theta are the given polar coordinates.
Rectangular coordinate y = r * sin(theta)
Here are the step-by-step solutions to the given problems:
1) Rectangular coordinates (4, -4)
r = sqrt(4^2 + (-4)^2) = sqrt(32) = 4 * sqrt(2)
theta = arctan((-4)/4) = -pi/4 (radians)
Polar coordinates: (4 * sqrt(2), -pi/4)
2) Rectangular coordinates (-3, -3)
r = sqrt((-3)^2 + (-3)^2) = sqrt(18) = 3 * sqrt(2)
theta = arctan((-3)/(-3)) + pi = pi/4 + pi = 5pi/4 (radians)
Polar coordinates: (3 * sqrt(2), 5pi/4)
3) Polar coordinates (-4, pi/6)
x = (-4) * cos(pi/6) = -4 * sqrt(3)/2 = -2 * sqrt(3)
y = (-4) * sin(pi/6) = -4 * 1/2 = -2
Rectangular coordinates: (-2 * sqrt(3), -2)
4) Polar coordinates (2, 3pi/4)
x = 2 * cos(3pi/4) = 2 * (-sqrt(2)/2) = -sqrt(2)
y = 2 * sin(3pi/4) = 2 * sqrt(2)/2 = sqrt(2)
Rectangular coordinates: (-sqrt(2), sqrt(2))
5) Polar coordinates (6, pi/3)
x = 6 * cos(pi/3) = 6 * 1/2 = 3
y = 6 * sin(pi/3) = 6 * sqrt(3)/2 = 3 * sqrt(3)
Rectangular coordinates: (3, 3 * sqrt(3))
You can use these formulas and steps to solve similar problems involving conversion between polar and rectangular coordinates.