If theta= pi/3 , then to convert to a Cartesian equation, let x =

A.(1/2)r
B.(square root of2/2)r
C.(square root of 3/2)r

x=r cos(θ)

=r cos(π/3)
=r cos(π/3*180/π)
=r cos(60°)
I'll let you complete with the calculator.

Y= root3 x

r2 = 6rcos(θ) + 7rsin(θ)

To convert an equation in polar coordinates to a Cartesian equation, you can use the following relationships:

x = r * cos(theta)
y = r * sin(theta)

In this case, we are given theta = pi/3.

To find the corresponding x-coordinate, we can substitute theta = pi/3 into the equation x = r * cos(theta):

x = r * cos(pi/3)

Next, we need to find the value of r. However, since we are only given theta and not the value of r, we are unable to determine the exact Cartesian equation.

The options you provided (A, B, C) are not sufficient to determine a specific value for x. In order to find the Cartesian equation, you would need to know the value of r as well.