the cartesian coordinates of a point on a circle are (1.5m, 2.0m). what are the point;s polar coordinates (r, degree) of this point?
To find the polar coordinates (r, θ) of a point on a circle given its Cartesian coordinates (x, y), you can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y / x)
In this case, the Cartesian coordinates are (1.5m, 2.0m).
To find r, we substitute the values of x and y into the formula:
r = √((1.5m)^2 + (2.0m)^2)
= √(2.25m^2 + 4.0m^2)
= √(6.25m^2)
= 2.5m
Next, to find θ, we substitute the values of x and y into the formula:
θ = arctan(2.0m / 1.5m)
≈ arctan(1.333...)
To calculate the arctan of 1.333..., you can use a scientific calculator or an online calculator.
Therefore, the polar coordinates (r, θ) of the point (1.5m, 2.0m) on the circle are approximately (2.5m, arctan(1.333...)).