What is the slope of the line normal to the tangent line of #f(x) = tanx+sin(x-pi/4) # at # x= (5pi)/6 #?

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Answer 1 · 2017-12-03T12:46:51

Slope of the normal to the tangent line is #-0.93#

Slope of the tangent is #f'(x)or f'((5pi)/6)#

#f(x)=tanx + sin(x-pi/4)#

#:.f'(x)=sec^2x + cos(x-pi/4)#

#:.f'((5pi)/6)=sec^2((5pi)/6) + cos((5pi)/6-pi/4)#

#(5pi)/6=150^0 ; pi/4=45^0#

#:.f'((5pi)/6)=sec^2(150) + cos(150-45)# or

#:.f'((5pi)/6)=1.33 -0.26 ~~1.07 or m_t ~~ 1.07#

Slope of the tangent line is #m_t ~~ 1.07#

Slope of normal to the tangent line is #m_n=-1/m_t# or

#m_n= -1/1.07 ~~ -0.93#

Slope of the normal to the tangent line is #-0.93# [Ans]