Angle of displacement

Geometry Level 3

A stair case has the property such that it starts at point \(A (0,0)\) and travels in the pattern right, up, right, up, right, up. . . ad infinitum and ends up at point \(B(x,y)\).

It travels \(\cos\left(18^\circ \right)\) to the right, \(\cos^2\left(18^\circ \right)\) up, \(\cos^3\left(18^\circ \right)\) right, \(\cos^4\left(18^\circ \right)\) and so on indefinitely.

Find the angle \(\theta\) segment \(\overline{AB}\) forms with the \(x\)-axis in degrees.

Assume \(\theta<90^{\circ}\).


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