Calculus question

Question

y = 4x from rectangular to polar coordinates.

Answer 1

You can substitute the identities:

x = r cos θ

y = r sin θ

to get:

r sin θ = 4r cos θ

sin θ = 4 cos θ

sinθ/cosθ = 4

tan θ = 4

θ = tan^-1(4)

Therefore, the answer is b.

Answer 2

Substitute the following expressions for x and y into your equation and then simplify:

x = rcosθ

y = rsinθ

y = 4x

rsinθ = 4(rcosθ)

sinθ = 4cosθ

sinθ / cosθ = 4

tanθ = 4

θ = tan^-1(4)