Help------I'm confused. I am trying to convert the linear equation 4x+3y-10=0 to polar form. Thus far, I have 2= r cos(theta -?????). I understand that I must get the arctan of 3/4 but I get the answer of 36.9. Is this correct and if not--what am I doing wrong.

Thanks

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°.