PLEASE HELP!
Transform polar equation to an equation in Cartesian (rectangular) coordinates. Then identify where it locate on the graph.
r sin θ = 4
To convert the given polar equation, r sin θ = 4, to Cartesian (rectangular) coordinates, we use the following formulas:
x = r cos θ
y = r sin θ
Substituting these formulas into the given polar equation, we get:
r sin θ = 4
(r)(sin θ) = 4
(r)(y / r) = 4
y = 4
So, the Cartesian equation corresponding to the polar equation r sin θ = 4 is simply y = 4.
The equation y = 4 represents a horizontal line that passes through the y-axis at the value y = 4. This line is parallel to the x-axis and does not depend on the value of x. So, no matter what the value of x is, y will always be equal to 4. On the graph, this line will be a horizontal line passing through the point (0, 4).