What is the slope of the polar curve f(theta) = theta - sectheta+thetasin^3theta at theta = (7pi)/12?

1 Answer
Mar 21, 2018

f'((7pi)/12)=-13.8459

Explanation:

Given:
f(theta)=theta-sectheta+thetasin^3theta
Differentiating wrt theta
f'(theta)=1-secthetatantheta+theta(3sin^2theta)costheta+sin^3theta
=1-1/costhetasintheta/costheta+sin^3theta+3thetasin^2thetacostheta
theta=(7pi)/12=1.8326

(7pi)/12=pi-(5pi)/12
costheta=cos(pi-(5pi)/12)=-cos((5pi)/12)=-0.2588
sintheta=sin(pi-(5pi)/12)=sin((5pi)/12)=0.9659
Substituting the values in f'(theta)

f'((7pi)/12)=1-1/-0.2588xx0.9659/-0.2588+0.9659^3+3xx1.8326xx0.9659^2(-0.2588)
f'((7pi)/12)=-13.8459