Question

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

Answer 1

Step-by-step explanation

Step 1:

Given data

`\theta\text{ = 45}`

Step 2:

Write the equations relating polar to rectangular coordinates are

`\theta\text{= arc}\tan ((y)/(x))\text{ or }\tan (\theta)\text{ = }(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{ = }(y)/(x) \\ \tan \text{ 45 = 1} \\ 1\text{ = }(y)/(x) \\ \text{Cross multiply} \\ y\text{ = x} \end{gathered}`

Final answer

y = x