Question

Convert the polar equation θ = 60° to a Cartesian equation

Answer 1

Answer:

y = tan(60°)x = (√3)x

Step-by-step explanation:

The usual translation between polar and rectangular coordinates is ...

... y = r·sin(θ)

... x = r·cos(θ)

If we solve the second equation for r, we get

... x/cos(θ) = r

Now, we can substitute this into the first equation with the result ...

... y = (x/cos(θ))·sin(θ) = x·tan(θ)

Our polar equation is θ = 60°, so we can substitute this value into the relation we have for x and y:

... y = x·tan(60°)

... y = (√3)x

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The portion of the line in the 3rd quadrant corresponds to r values that are negative. The given polar equation has no restriction against that.