anonymous
  • anonymous
Find an equation of the tangent line to the curve y=sin(7x)+cos(6x) at the point (pi/6,y(pi/6))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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hartnn
  • hartnn
do you know how to find slope of tangent at a point ?
anonymous
  • anonymous
I will first take the derivative of that equation and then plug in x. For some reason I'm still not getting the correct answer to this problem.
hartnn
  • hartnn
show your work, i'll spot the error.

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hartnn
  • hartnn
this way it'll get solved faster
anonymous
  • anonymous
7cos(7x)−6sin(6x) is the derivative. So plugging in pi/6 for x to get the slope. We get -6.062177826
hartnn
  • hartnn
ok, i get the same thing, thats your slope
anonymous
  • anonymous
So putting this is slope intercept form you get \[Y=-6.062177826x+b\] My only concern is with the y value being y(pi/6)
hartnn
  • hartnn
yes, to get y(pi/6) put x=pi/6 in y sin(7pi/6)+cos(6pi/6) = ...
anonymous
  • anonymous
wait where am i putting the pi/6?
hartnn
  • hartnn
to get y(pi/6) from y(x) =sin(7x)+cos(6x) just replace x = pi/6 there
anonymous
  • anonymous
so -1.5?
hartnn
  • hartnn
yup so point is (pi/6, -1.5) with slope = -6.06 now can u find the equation of line ?
anonymous
  • anonymous
So b=1.674148887 (I kept the full value of the slope in.) So the answer would be y=-6.062177826x+1.674148887
hartnn
  • hartnn
yes, i get the same answer.
anonymous
  • anonymous
Thank you very much for your help today.
hartnn
  • hartnn
welcome very much :)

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