Convert to Polar: y/x = 4
A. r = 2
B. r = 16
C. Θ = 76
D. Undefined
tanθ = 4
θ = arctan(4)
(C)
To convert the equation y/x = 4 to polar form, we can use the following formulas:
r = √(x^2 + y^2)
θ = arctan(y/x)
Let's calculate the values step-by-step.
1. Calculate r:
r = √(x^2 + y^2)
= √(1^2 + (4r)^2)
= √(1 + 16r^2)
2. Calculate θ:
θ = arctan(y/x)
= arctan(4r/1)
= arctan(4r)
Therefore, the correct option for the polar form of the equation y/x = 4 is:
C. Θ = arctan(4r)
To convert the equation y/x = 4 to polar form, we can use the following relationships:
r = √(x^2 + y^2) (to find the value of r)
θ = atan(y/x) (to find the value of θ, where atan represents the inverse tangent function)
Let's proceed with the conversion:
Given: y/x = 4
First, we can rewrite the equation as y = 4x.
Now, substituting this value of y in the formula for r, we get:
r = √(x^2 + (4x)^2)
= √(x^2 + 16x^2)
= √(17x^2)
= √(17)x
Since we want to find r, which is the distance from the origin to the point (x, y), we can see that r is dependent on x. This indicates that the value of r can vary depending on the value of x.
Hence, the correct answer is D. Undefined, as r is not a fixed value.