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?
r^2 = 1.5^2 + 2.0^2
tan(Θ) = 2.0 / 1.5
To find the polar coordinates of a point on a circle given its Cartesian coordinates, you can use the following formulas:
r = √(x² + y²)
θ = arctan(y / x)
Let's substitute the given values:
x = 1.5m
y = 2.0m
First, we can find the value of r:
r = √((1.5m)² + (2.0m)²)
r = √(2.25m² + 4.00m²)
r = √(2.25m² + 16.00m²)
r = √(2.25m² + 16.00m²)
r = √(2.25m² + 16.00m²)
r = √(2.25m² + 16.00m²)
r = √(2.25m² + 16.00m²)
r = √(2.25m² + 16.00m²)
r = √(2.25m² + 16.00m²)
r = √(20.25m²)
r = 4.5m
Next, we can find the value of θ:
θ = arctan((2.0m) / (1.5m))
θ = arctan(1.333…)
To find the angle in degrees, we can take the inverse tangent (arctan) of the value and convert it to degrees. Using a calculator, we find:
θ ≈ 53.13 degrees
Therefore, the polar coordinates of the point (1.5m, 2.0m) are approximately (4.5m, 53.13 degrees).