# What is the slope of the polar curve #f(theta) = theta - sec^2theta+costheta # at #theta = (7pi)/12#?

##### 1 Answer

#### Explanation:

The slope of the polar curve at

To find

#y=r sintheta = (theta - sec^2theta+costheta)(sintheta)#

#(dy)/(d theta) = (1 - 2sec^2(theta)tan(theta) - sintheta)(sintheta) + (theta-sec^2theta+costheta)(costheta)#

Evaluating this at

#x=r costheta = (theta - sec^2theta + costheta)(costheta)#

#(dx)/(d theta) = (1 - 2sec^2(theta)tan(theta) - sintheta)(costheta) + (theta-sec^2theta+costheta)(-sintheta)#

Evaluating this at

Therefore, the slope of the line tangent to