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

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Answer 1 · 2018-04-10T13:34:21

the slope of the tangent is #2.57#

#r=2theta+3cos(theta/2-(2pi)/3)#

#(dr)/(d theta)=2-3/2sin(theta/2-(2pi)/3)#

At #theta=(3pi)/4#,

#(dr)/(d theta)=2-3/2sin((3pi)/8-(2pi)/3)#

#(dr)/(d theta)=2-3/2sin(-(7pi)/8)#

#(dr)/(d theta)=2.57#

Therefore, the slope of the tangent is #2.57#