# What is the slope of the polar curve #f(theta) = theta + cottheta+thetasin^2theta # at #theta = (3pi)/8#?

##### 2 Answers

Jul 5, 2016

#### Explanation:

- The slope of any curve/function at a certain point is always the function's first derivative.

Hence, the slope of#f(theta)=f'(theta)# #f'(theta)=1-csc^2theta+theta*2sintheta*costheta+sin^2theta#

#=1-csc^2theta+thetasin2theta+sin^2theta# - Therefore, the slope at
#theta=(3pi)/8 # is

#f'((3pi)/8)=1-csc^2((3pi)/8)+(3pi)/8sin2((3pi)/8)+sin^2((3pi)/8)#

#=1-1.17+0.83+0.85#

#=1.51#

Jul 5, 2016

Added graph

#### Explanation:

The graphing package I am using must have a slight error in the coding as the point does not sit exactly on the plotted line.

However; the uploaded image should give you a rough guide.