What is the slope of the tangent line of r=thetacos(-3theta+(7pi)/4) at theta=(-2pi)/3?

1 Answer
Jun 27, 2018

((1+2pi)sqrt2)/2

Explanation:

r=thetacos((7pi)/4-3theta)

color(blue)(d/(d(theta)))r=color(blue)(d/(d(theta)))(thetacos((7pi)/4-3theta)

(dr)/(d(theta))=cos((7pi)/4-3theta)+3thetasin((7pi)/4-3theta)

cos((7pi)/4-3((-2pi)/3))+3((-2pi)/3)sin((7pi)/4-3((-2pi)/3))

cos((7pi)/4+2pi)-2pisin((7pi)/4+2pi)

cos((7pi)/4)-2pisin((7pi)/4)

sqrt2/2-2pi*-sqrt2/2

((1+2pi)sqrt2)/2