PLEASE HELP!
Transform polar equation to an equation in Cartesian (rectangular) coordinates. Then identify where it locate on the graph.
r sin θ = 4
r,theta>>x,y
x= r*cosTheta= 4/sintheta *costheta=4ctnTheta
y= r*sinTheta=4 tan theta
check me. It appears to be in the y>0 area, symmetric about the y axis.
To transform a polar equation to a Cartesian (rectangular) equation, you can use the following relationships:
1. r = sqrt(x^2 + y^2)
2. x = r * cos(θ)
3. y = r * sin(θ)
Given the polar equation r sin θ = 4, we can substitute the values of r and sin(θ) using the relationships above:
sqrt(x^2 + y^2) * sin(θ) = 4
Now, let's solve for y:
y = (4 * cos(θ)) / sin(θ)
This equation represents the Cartesian equation that corresponds to the given polar equation.
To identify where this equation locates on the graph, we can analyze its behavior. Since the expression involves both sin(θ) and cos(θ), the resulting graph will have a combination of both sine and cosine functions. The equation's graph generally resembles a sinusoidal curve with varying amplitudes and frequencies depending on the values of θ.
It's important to note that the specific location on the graph will depend on the range of θ values. If the range of θ is not specified, the equation represents an entire curve extending infinitely in all directions.