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

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Answer 1 · 2018-06-27T06:47:39

#((1+2pi)sqrt2)/2#

#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#