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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
    • 2 years ago
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    do you know how to find slope of tangent at a point ?

  2. kiszer4148
    • 2 years ago
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    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
    • 2 years ago
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    show your work, i'll spot the error.

  4. hartnn
    • 2 years ago
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    this way it'll get solved faster

  5. kiszer4148
    • 2 years ago
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    7cos(7x)−6sin(6x) is the derivative. So plugging in pi/6 for x to get the slope. We get -6.062177826

  6. hartnn
    • 2 years ago
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    ok, i get the same thing, thats your slope

  7. kiszer4148
    • 2 years ago
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    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
    • 2 years ago
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    yes, to get y(pi/6) put x=pi/6 in y sin(7pi/6)+cos(6pi/6) = ...

  9. kiszer4148
    • 2 years ago
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    wait where am i putting the pi/6?

  10. hartnn
    • 2 years ago
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    to get y(pi/6) from y(x) =sin(7x)+cos(6x) just replace x = pi/6 there

  11. kiszer4148
    • 2 years ago
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    so -1.5?

  12. hartnn
    • 2 years ago
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    yup so point is (pi/6, -1.5) with slope = -6.06 now can u find the equation of line ?

  13. kiszer4148
    • 2 years ago
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    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
    • 2 years ago
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    yes, i get the same answer.

  15. kiszer4148
    • 2 years ago
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    Thank you very much for your help today.

  16. hartnn
    • 2 years ago
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    welcome very much :)

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