The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below. x2+y2−4x=0

a.  r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ

B. r = 4cosθ

Step-by-step explanation:

Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).

x = rcosθ and y = rsinθ.

Substituting the value of x and y in their polar form into the given expression we have;

x²+y²−4x=0

( rcosθ)²+( rsinθ)²-4( rcosθ) = 0

Expand the expressions in parenthesis

r²cos²θ+r²sin²θ-4rcosθ = 0

r²(cos²θ+sin²θ)-4rcosθ = 0

From trigonometry identity, cos²θ+sin²θ =1

The resulting equation becomes;

r²(1)-4rcosθ = 0

r²-4rcosθ = 0

Add 4rcosθ to both sides of the equation

r²-4rcosθ+4rcosθ = 0+4rcosθ

r² = 4rcosθ

Dividing both sides by r

r²/r = 4rcosθ/r

r = 4cosθ

Hence the correct equation in polar coordinates is r = 4cosθ

Idk i am in 5th grade lol

Period is the time it takes for one “cycle” to complete. in the parent sine function, period is 2*pi since sin(0) = 0, sin(pi/2) = 1, sin(pi) = 0, sin(3pi/2) = -1, and sin(2pi) = 0. at that point, the sequence repeats itself. i’m not sure if your graph is similar to the sine function since you didn’t provide a picture, but you can find the period by looking at a graph.