A surveyor records the polar coordinates of the location of a landmark as (40, 62°). What are the rectangular coordinates? Round each coordinate to the nearest hundredth.
first recall that the form of polar coordinate is
(r, θ)
to convert polar coordinate to rectangular coordinate, we do this:
(r*cos θ , r*sin θ)
in the problem, r = 40 and θ = 62. thus,
(r*cos θ , r*sin θ)
(40*cos 62 , 40*sin 62)
(18.78 , 35.32)
hope this helps~ :)
Thank YOU!!!
To convert polar coordinates to rectangular coordinates, we use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
Given the polar coordinates (40, 62°), we can substitute into the formulas to find the rectangular coordinates:
x = 40 * cos(62°)
y = 40 * sin(62°)
Using a calculator, we can find:
x ≈ 19.56
y ≈ 31.61
Therefore, the rectangular coordinates are approximately (19.56, 31.61).
To find the rectangular coordinates from the polar coordinates, we can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
Where:
r is the length of the vector from the origin to the point
theta is the angle (in degrees) measured counterclockwise from the positive x-axis to the vector
In this case, the given polar coordinates are (40, 62°). Let's substitute the values into the formulas:
x = 40 * cos(62°)
y = 40 * sin(62°)
Using a calculator, find the approximate values of cos(62°) and sin(62°):
cos(62°) ≈ 0.466
sin(62°) ≈ 0.885
Now, substitute these values back into the formulas:
x ≈ 40 * 0.466 ≈ 18.64
y ≈ 40 * 0.885 ≈ 35.4
Rounding each coordinate to the nearest hundredth, the rectangular coordinates are approximately (18.64, 35.4).