A circus trapeze consists of a bar suspended by two parallel ropes, each of length ?=2.1m, 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 2.25 of the performer's weight.

Give your answer to two decimal places.