Answer:
a) There is no algebraic method for finding θ in terms of n
b) should be a = r(1 -cos(θ))
Step-by-step explanation:
Algebraic methods have been developed for solving trig functions and polynomial functions individually, but not in combination. In general, the solution is easily found numerically, but not analytically.
You would be looking for the numerical solution to ...
f(n, θ) = 0
where f(n, θ) can be ...
f(n, θ) = θ - (1/2)sin(2θ) - π/n
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The attached shows Newton's method iterative solutions for n = 3 through 6:
for n = 3, θ ≈ 1.3026628373
for n = 4, θ ≈ 1.15494073001
...
