Question $12(1$ point$)$

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A circus trapeze consists of a bar suspended by two parallel ropes, each of length $=2\mathrm{.}9$m$,$ allowing performers to swing in a vertical circular arc. Suppose a performer with mass m holds the bar and steps off an elevated platform, starting from rest with the ropes at an angle i$$with respect to the vertical. Suppose the size of the performer's body is small compared to the length $,$ she does not pump the trapeze to swing higher, and air resistance is negligible.

Determine the value of cos $($i$)$ such that the force needed to hang on at the bottom of the swing is $2\mathrm{.}00$ of the performer's weight.$$

Give your answer to two decimal places.$$

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