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## kiszer4148 2 years ago Find an equation of the tangent line to the curve y=sin(7x)+cos(6x) at the point (pi/6,y(pi/6))

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1. hartnn

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

2. kiszer4148

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.

3. hartnn

show your work, i'll spot the error.

4. hartnn

this way it'll get solved faster

5. kiszer4148

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

6. hartnn

ok, i get the same thing, thats your slope

7. kiszer4148

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)

8. hartnn

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

9. kiszer4148

wait where am i putting the pi/6?

10. hartnn

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

11. kiszer4148

so -1.5?

12. hartnn

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

13. kiszer4148

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

14. hartnn

yes, i get the same answer.

15. kiszer4148

Thank you very much for your help today.

16. hartnn

welcome very much :)

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