# How do I Calculate the odds ratio for a circular predictor variable using the coefficient(s) of a logistic regression?

Using a logistic regression I have modelled the habitat characteristics of a dataset existing out of GPS positions. To visualize the results I want to calculate the odds ratio for each value in my predicting variables. However, one of my variables is circular; aspect (in radians).

Aspect is included in the model as two separate variables, namely sin(aspect) and cos(aspect) to account for that.

I would expect to have to calculate the odds ratio for aspect as $y= e$ $\beta_1 \sin(\chi)+\beta_2\cos(\chi)$. Unfortunately the result I am getting does not match what can naturally be expected; a western orientation is preferred whilst my expectation is north/ northeast.

As I haven't found any literature on calculating the odds ratio for a circular variable, I don't actually know if the above mentioned equation is correct. Therefore my question is; how do I calculate the odds ratio for the circular variable; aspect?

Edit: Some clarification on the use of a circular predictor in linear regression is already offered in these posts;

Use of circular predictors in linear regression

Predict magnitude from angle in linear regression

Edit: Some literature that explains the use, or uses, circular variables as predictor(s):

Cox, N. J. (2006). Speaking Stata: in praise of trigonometric predictors. Stata Journal, 6(4), 561-579.

Gustine, D. D. (2005). Plasticity in selection strategies of woodland caribou (Rangifer tarandus caribou) during winter and calving (Doctoral dissertation, University of Northern British Columbia).

Gutiérrez, D., Fernández, P., Seymour, A. S., & Jordano, D. (2005). Habitat distribution models: are mutualist distributions good predictors of their associates?. Ecological applications, 15(1), 3-18.

Jammalamadaka, S. R., & Lund, U. J. (2006). The effect of wind direction on ozone levels: a case study. Environmental and Ecological Statistics, 13(3), 287-298.

Steger, S., Brenning, A., Bell, R., & Glade, T. The propagation of inventory-base dpositional errors into statistical landslide susceptibility models.

Okay, it seems that my calculation for the odds ratio is correct.

I grouped aspect in classes and replaced the numerical variables temporarily in the model with the categorical to see if the effect would be roughly the same and it is, west is still preferred most.