a. Show graphically that the equation cot x = sin x has a root,, which is such

a. Show graphically that the equation cot x = sin x has a root,α, which is such that 0 < α < π/2.

b. Show that the equation in part a can be rearranged as x = sin⁻¹ √cos x.

c. Using an iterative formula based on the equation in part b, with an initial value of 0.9, find the value of correct to 2 decimal places. Give the value of each iteration to an appropriate number of decimal places.

d. The equation given in part a can be rearranged in other ways.
Find an example of a formula, based on a different rearrangement of the equation given in part a, that also converges to the value of  α, with an initial value of 0.9, in fewer iterations than the formula used in part c.