# Unit Vectors and tangent line

## Homework Statement

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

## The Attempt at a Solution

I took the derivative of y=2sinx and got y'=2cosx. Then subbed in $$\pi$$/6 and got slope=$$\sqrt{3}$$. 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.

Defennder
Homework Helper
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?

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.

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:
Defennder
Homework Helper
Don't see how you got that answer. Might want to re-check your working.