the wrapping function

Question

what is the wrapping function of 7pi/6

Answer 1

The wrapping function w(θ) is defined by w(θ) = (cosθ, sinθ).  

 

If θ ≥ 0, then w(θ) is the point on the unit circle arrived at if we start at (1,0) and travel an arc of length θ in the counterclockwise direction.

 

If θ < 0, then w(θ) is the point on the unit circle arrived at if we start at (1,0) and travel an arc of length -θ in the clockwise direction.  

 

w(7π/6) = (cos(7π/6), sin(7π/6)) = (-√3/2, -1/2) 

Answer 2

Hi Dylan,

 

 

what is the wrapping function of 7pi/6

 

I highly suggest that you draw a unit circle and fill in all the radian and degree values.  It will make this process a lot easier because you'll have visual representation.

 

pi/6 is 30°   Quadrant I

2pi/6 = pi/3 is 60°  Quadrant I

3pi/6 = pi/2 is 90°  y-axis

4pi/6=2pi/3 is 120°  Quadrant II

5pi/6  is 150°  Quadrant II

6pi/6 = pi is 180°  x-axis

7pi/6 is 210° Quadrant III

 

ANSWER:  7pi/6 is 210° Quadrant III