Write the equation of the line tangent to the graph of r=2cosTheta when Theta =(4pi )/(3)

To find the equation of the line tangent to the graph of when , we need to follow these steps:1. Find the slope of the tangent line at the given point.2. Find the equation of the tangent line using the point-slope form.Step 1: Find the slope of the tangent line at the given point.The slope of the tangent line can be found by taking the derivative of the given equation with respect to and evaluating it at the given point.Given equation: Taking the derivative with respect to : Evaluating the derivative at : So, the slope of the tangent line at is .Step 2: Find the equation of the tangent line using the point-slope form.The point-slope form of a line is given by: We need to find the coordinates of the point on the graph of when .Substituting into the given equation: So, the point on the graph is .Now, we can substitute the slope and the coordinates of the point into the point-slope form: Simplifying the equation: Therefore, the equation of the line tangent to the graph of when is: