Find an equation of the tangent line to the curve
y=sin(7x)+cos(6x) at the point (pi/6,y(pi/6))

Question

Find an equation of the tangent line to the curve
y=sin(7x)+cos(6x) at the point (pi/6,y(pi/6))

hartnn · Answer

do you know how to find slope of tangent at a point ?

anonymous · Answer

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 · Answer

show your work, i'll spot the error.

hartnn · Answer

this way it'll get solved faster

anonymous · Answer

7cos(7x)−6sin(6x) is the derivative. So plugging in pi/6 for x to get the slope. We get -6.062177826

hartnn · Answer

ok, i get the same thing, thats your slope

anonymous · Answer

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 · Answer

yes, to get y(pi/6)
put x=pi/6 in y
sin(7pi/6)+cos(6pi/6) = ...

anonymous · Answer

wait where am i putting the pi/6?

hartnn · Answer

to get y(pi/6) from y(x) =sin(7x)+cos(6x) 
just replace x = pi/6 there

anonymous · Answer

so -1.5?

hartnn · Answer

yup
so point is (pi/6, -1.5) with slope = -6.06
now can u find the equation of line ?

anonymous · Answer

So b=1.674148887 (I kept the full value of the slope in.)
So the answer would be y=-6.062177826x+1.674148887

hartnn · Answer

yes, i get the same answer.

anonymous · Answer

Thank you very much for your help today.

hartnn · Answer

welcome very much :)