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

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Answer 1 · 2018-07-26T12:26:19

Slope of tangent at # pi/4# is #1.09#

#r= theta- sin(theta/3- (2 pi)/3) ; theta = pi/4#

#(dr)/(d theta) = 1 - cos (theta/3-(2 pi)/3)*1/3#

#(dr)/(d theta)(pi/4) = 1 - cos ((pi/4)/3-(2 pi)/3)*1/3# or

#(dr)/(d theta)(pi/4) = 1 - cos (pi/12-(2 pi)/3)*1/3#or

#(dr)/(d theta)(pi/4) = 1 - cos (-1.8326)*1/3#or

#=(dr)/(d theta)(pi/4) = 1 - (-0.2588)*1/3#

#=(dr)/(d theta)(pi/4) ~~ 1.086#

Slope of tangent at # pi/4# is #1.09# [Ans]