Question

Transform each polar equation to an equation in rectangular form.

Theta = pi/3

Part I: Use the conversion rules to express x and y in terms of r. You should have two equations after this step.

Part II. Use the ratio (y/x) to find the slope of the line defined by this equation.

Part III: Write the equation of the line in slope-intercept form.

Answer 1

that is the graph of theta = pi/3 . do you see why? r is allowed to vary
so you have polar coordinates (r, pi/3).
Now in rectangular coordinates, do you see what you have to do?

Answer 2

that is a line through the center with an angle pi/3, and the line has slope tan (pi/3).
That means you want y = tan(pi/3) * x

Answer 3

another way to do this, in your list of conversion rules you have
arctan (y/x) = theta . so you can plug in theta = pi/3 into
arctan (y/x) = theta . if you dont reply im leaving the question