

I want to aim a desk lamp by specifying where it should point. P(x,y)
is where to aim the lamp, c is the length of the flexible part of the
neck, a is an additional rigid distance to the central axis of the lamp
hood, and f is the angle to bend the neck. The initial equation was
huge and ugly, but I managed to simplify it considerably, to this form:
(x  c/f) * sin(f) + y * cos(f) = a
But now I'm stuck. Variables a, c, x, and y are given, and I need to
solve for f. I plugged it into Wolfram Alpha, but it gave up. I don't
even know if a paid subscription would find a solution, and I would
hardly use the service enough to justify a subscription anyway. Does
anyone have an idea of how to proceed with the equation? Or should I
gamble that Wolfram Alpha Pro can solve it and pay for one month?
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