The rectangular coordinates of a point are given (-5,-5root3). Find polar coordinates of the point. Express theta in radians.
Answer must be in form
(Type an ordered pair. Type an exact answer in terms of pi.Use integers or fractions for any numbers in the expression. Type the coordinate for theta in radians between 0 and 2pi)
My answer is (10,pi/3)but website is not accepting it . tell me mistake i am doing and the right answer
my bad thank you sir
No problem :) You are welcome.
To find the polar coordinates of a point given its rectangular coordinates, we can use the following formulas:
r = sqrt(x^2 + y^2)
theta = arctan(y/x)
Given that the rectangular coordinates of the point are (-5, -5√3), we can substitute these values into the formulas to find the polar coordinates.
First, let's calculate r:
r = sqrt((-5)^2 + (-5√3)^2)
= sqrt(25 + 75)
= sqrt(100)
= 10
Now, let's calculate theta:
theta = arctan((-5√3)/(-5))
= arctan(√3)
= π/3
So, the polar coordinates of the point are (10, π/3) in the form of an ordered pair, where r = 10 and theta = π/3 radians.
If the website is not accepting this answer, it is possible that it requires the answer in a different format. Double-check the format specified by the website or consider converting theta to a decimal form.
r^2 = 25 +25*3 = 100
so
r = 10
tan theta = sqrt3 in quadrant III
60 degrees below x axis
pi + pi/3 = 4 pi/3
you are in third quadrant because x and y are negative