# Unit Vectors and tangent line

1. Sep 12, 2008

### 2RIP

1. The problem statement, all variables and given/known data
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.

2. Relevant equations

3. 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.

2. Sep 12, 2008

### Defennder

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. Sep 12, 2008

### kmikias

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. Sep 12, 2008

### 2RIP

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: Sep 12, 2008
5. Sep 12, 2008

### Defennder

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