Determine Quadrant using Circular Package R -

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can explain me how 1 can determine quadrant mean lies in when circular stats function used? example below

> mean(df3[[1]]) circular data:  type = angles  units = degrees  template = geographics  modulo = asis  0 = 1.570796  rotation = clock  [1] 152.6511

usually quadrant determined mathematically. not sure how apply mathematical understanding (below) circular function in r

determining quadrant

  • sin +, cos + : mean angle computed directly.
  • sin +, cos - : mean angle = 180 – θr
  • sin -, cos - : mean angle = 180 + θr
  • sin -, cos + : mean angle = 360 - θr

basically question this, when follow rules above when number circular package?

i took example ?mean.circular , ran code. since that's not reproducible example, posted dput output below image:

> findinterval( mean(x) , seq(0, 2*pi, by=pi/2) ) [1] 1 > plot(mean(x))

enter image description here

> x <- circular::circular(runif(50, circular(0), pi)) > mean.circular(x) circular data:  type = angles  units = radians  template = none  modulo = asis  0 = 0  rotation = counter  [1] 1.456398 > x circular data:  type = angles  units = radians  template = none  modulo = asis  0 = 0  rotation = counter   [1] 2.327040536 2.785825681 1.308066172 0.465629700 1.591991415  [6] 2.799895638 0.597101630 1.532398268 2.286539493 2.406796452 [snipped several more lines] > str(x) classes 'circular', 'numeric'  atomic [1:50] 2.327 2.786 1.308 0.466 1.592 ...   ..- attr(*, "circularp")=list of 6   .. ..$ type    : chr "angles"   .. ..$ units   : chr "radians"   .. ..$ template: chr "none"   .. ..$ modulo  : chr "asis"   .. ..$ 0    : num 0   .. ..$ rotation: chr "counter"

dput output:

> dput(x) structure(c(2.3270405356074, 2.78582568050163, 1.30806617224081,  0.46562970044316, 1.59199141527826, 2.79989563818328, 0.5971016303539,  1.53239826820734, 2.28653949278211, 2.40679645204717, 1.89535428259936,  2.93137660453899, 0.0177478829505632, 1.42734595196813, 1.87201844464804,  0.695967970430947, 2.04070832419577, 0.550663977456403, 2.92634734087854,  0.958306068791458, 2.84969662093696, 2.51629270013684, 2.59782748619366,  1.02971903657107, 0.561164568631031, 2.23073552882588, 1.22498917136169,  2.9371640847422, 0.457753977096242, 0.739334808330959, 0.216332478818938,  0.405318219633614, 1.99178154032455, 0.113127579417766, 0.894931514015444,  2.35655867340775, 0.246653277344759, 2.70813517178582, 2.18657670803946,  0.0214119953469805, 0.95793239635793, 2.22692798316346, 0.582003007195641,  0.611648808005097, 2.67776878946411, 0.00293802811780693, 2.99580227692684,  0.809807730553898, 0.936388196372667, 0.378983006826294), circularp = structure(list(     type = "angles", units = "radians", template = "none", modulo = "asis",      0 = 0, rotation = "counter"), .names = c("type", "units",  "template", "modulo", "zero", "rotation")), class = c("circular",  "numeric"))

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