To convert a linear equation from Cartesian form to polar form, follow these steps:
Step 1: Express the given equation in terms of x and y.
Given equation: 4x + 3y - 10 = 0
Step 2: Replace x with r cos(theta) and y with r sin(theta).
Substituting: 4(r cos(theta)) + 3(r sin(theta)) - 10 = 0
Step 3: Simplify the equation.
4r cos(theta) + 3r sin(theta) - 10 = 0
Step 4: Rearrange the terms to isolate r.
4r cos(theta) + 3r sin(theta) = 10
r(4 cos(theta) + 3 sin(theta)) = 10
r = 10 / (4 cos(theta) + 3 sin(theta))
So, the correct polar form of the equation is r = 10 / (4 cos(theta) + 3 sin(theta)).
Now, let's find the value of theta. From your question, you mentioned finding arctan(3/4) and getting an answer of 36.9. However, the value of arctan(3/4) is approximately 36.87 degrees.
Thus, it seems like you made a rounding error in your calculation. The correct value of arctan(3/4) is approximately 36.87 degrees, which can be written as theta = 36.87°.
Therefore, the final polar form of the equation is r = 10 / (4 cos(theta) + 3 sin(theta)), where theta = 36.87°.