A. solve for in terms of "n"(derivation of equation below)b. based on your answer inpart a, if or find "a" as a function ofr & n. (find f(r, n)=a).alternately, if a+b=r, we can write then solve for "a" in terms of r and nshow all work and reasoning. solve analytically if possible

  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

...

7. 153.86 ft

8. 12.56 ft

9. 78.5 m

10. 379.94 in

11. 132.665 m

12. 12.56 yd

13. 226.865 ft

14. 113.04 ft

15. 63.585 ft

16. 254.34 m

17. 50.24 cm

step-by-step explanation:

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by definition, an arc subtended by a central angle of some given measure has the same measure. so .