Unit Vectors and tangent line

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  • #1
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Homework Statement


Find the unit vectors that are parallel to the tangent line to the curve y=2sinx at the point ([tex]\pi[/tex]/6, 1). Thereafter, find the unit vectors that are perpendicular to the tangent line.


Homework Equations



The Attempt at a Solution


I took the derivative of y=2sinx and got y'=2cosx. Then subbed in [tex]\pi[/tex]/6 and got slope=[tex]\sqrt{3}[/tex]. After this, I was totally confused about what to do next since I don't know how to put the function with respect to i, j. Thanks in advance.
 

Answers and Replies

  • #2
Defennder
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First thing you should note is that dy/dx tells you how the unit vector x-y components are related to each other. Draw the tangent line at pi/6, and a really small right-angle triangle with the vertical length denoted dy and horizontal length dx. So, see what to do next?
 
  • #3
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you have slop which is rise over run . so rise will be j-hat and run will be i-hat.you don't have to find k-hat.just simplify square root of 3.
 
  • #4
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Oh yes, I think i got it now. Just to confirm is it (i+root3j) and (-i-root3j)? Thank you so much guys.
 
Last edited:
  • #5
Defennder
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Don't see how you got that answer. Might want to re-check your working.
 

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