1. (11.1.11) Find an arc length parametrization of the cycloid defined by xat a sin t...

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1. (11.1.11) Find an arc length parametrization of the cycloid defined by xat a sin t y = a a cost 0 t 2 with reference point (0, 0). - =(e- 2. Find lim r(t) where r(t) = = t-e -2t 2 2t + 3 3t 1' arctan(2t) S ( - ) - 2a [- (-) (-2), (1 1- 4a 4a 11. x = 2a cos-1 0s 8a Hint: use the identities cost = 2 cos with the fact that sin (1) 2 y = t (17) - (1-0062 (1/2) = 2 s(8a s) " 8a - 1 and sin t = 2 sin (2) cos (2) together 1. (11.1.11) Find an arc length parametrization of the cycloid defined by xat a sin t y = a a cost 0 t 2 with reference point (0, 0). - =(e- 2. Find lim r(t) where r(t) = = t-e -2t 2 2t + 3 3t 1' arctan(2t) S ( - ) - 2a [- (-) (-2), (1 1- 4a 4a 11. x = 2a cos-1 0s 8a Hint: use the identities cost = 2 cos with the fact that sin (1) 2 y = t (17) - (1-0062 (1/2) = 2 s(8a s) " 8a - 1 and sin t = 2 sin (2) cos (2) together