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.