How do you find the unit vectors that are parallel to the tangent line to the curve y = 2sinx at the point (pi/6,1)?

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Answer 1 · 2016-08-24T12:54:24

# +- < cos (pi/6), sin (pi/6) > =+-<1/2, sqrt 3/2>#

y'at# x = pi/6# is #2 cos (pi/6) = sqrt3#.

This direction #theta=psi# is given by #tan psi=sqrt 3#.

Inversely, #psi = tan^(-1) sqrt 3# is #pi/6#. For the opposite direction ,

it is #pi+pi/6#.

The unit vector in the direction #theta = pi/6# is

# < cos (pi/6), sin (pi/6) >#.

For the opposite direction, it is

#< cos(pi+pi/6), sin(pi+pi/6) >#

#=<-cos(pi/6),-sin(pi/6)># .