# 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.