Arrays Start at \$\pi\$
R, 59 53 bytes



function(x,i)x[0:1+i%/%pi]%*%c(a&lt;-cos(i%%pi/2)^2,1-a)


Try it online!

Nothing too clever here - just an R version of the formula in the question. 
Thanks @MickyT for saving a byte, and to @Giueseppe and indirectly @xnor for another two, and thanks to @RobinRyder for saving a further 3.