What is the slope of the polar curve #f(theta) = sectheta - csctheta # at #theta = (3pi)/4#?

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Answer 1 · 2018-05-03T13:11:54

Slope of the polar curve at #theta=(3pi)/4# is #0#

#f(theta)=sec theta - csc theta ; theta = (3pi)/4#

#f'(theta)=sec theta* tan theta -(- csc theta* cot theta)# or

#f'(theta)=sec theta* tan theta + csc theta* cot theta#

#cos ((3pi)/4) = -1/sqrt2 :. sec ((3pi) /4 ) = - sqrt 2#

#sin ((3pi)/4) = 1/sqrt2 :. csc ((3pi) /4 ) = sqrt 2#

#tan ((3pi)/4) = -1 :. cot ((3pi) /4 ) = -1#

#:. f'(theta)= (-sqrt2* -1) + ( sqrt2* -1)#

#:. f'(theta)= sqrt2 - sqrt 2 =0#

Slope of the polar curve at #theta=(3pi)/4# is #0# [Ans]