Write following equations in polar coordinate then graph them
Y=4X
To convert the equation y = 4x into polar coordinates, we need to express x and y in terms of r (distance from the origin) and θ (angle in radians).
The conversion can be done using the following equations:
x = r * cos(θ)
y = r * sin(θ)
Let's substitute these equations into y = 4x:
r * sin(θ) = 4 * (r * cos(θ))
Now, let's simplify this equation:
r * sin(θ) = 4r * cos(θ)
(sin(θ)) / (cos(θ)) = 4
To graph this equation, we can plot multiple points and connect them to form a curve. We will choose different values for θ within a certain range and calculate r for each θ using the given equation.
For example, let's choose three different values for θ: 0, π/4, and π/2.
For θ = 0:
(sin(0)) / (cos(0)) = 4
0 = 4 (which is not true)
For θ = π/4:
(sin(π/4)) / (cos(π/4)) = 4
(1/√2) / (1/√2) = 4
1 = 4 (which is not true)
For θ = π/2:
(sin(π/2)) / (cos(π/2)) = 4
1/0 = 4 (which is not defined)
From these calculations, we can see that the equation y = 4x doesn't produce any valid polar coordinates for the given values of θ.
Therefore, the graph of y = 4x in polar coordinates is empty or undefined.