Question

Convert the polar equation∅=45° to a Cartesian equation.Choices:y=xy=√2xy=2x

Answer 1

Explanation

Step 1:

Given data

$\theta\text{ = 45}$

Step 2:

Write the equations relating polar to rectangular coordinates are

$\theta\text{= arc}\tan (\frac{y}{x})\text{ or }\tan (\theta)\text{ = }\frac{y}{x}\text{ and r = }\sqrt[]{x^2+y^2}$

Since your polar equation has no "r" we will not need the last equation.

Step 3:

$\text{Substitute the value of }\theta\text{ = 45}$

Therefore

$\begin{gathered} \tan 45\text{ = }\frac{y}{x} \\ \tan \text{ 45 = 1} \\ 1\text{ = }\frac{y}{x} \\ \text{Cross multiply} \\ y\text{ = x} \end{gathered}$

Final answer

y = x