Problemas Complementarios Curvas Planas Determine T,N y
para las curvas planas
1. r(t) ti lncos t j, / 2 t / 2
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Solución
sent r '(t) i j i tan t j cos t r '(t) 12 tan t sec 2 t sec t sec t, / 2 t / 2 2
T
v 1 tan t i j cos t i sent j; v sec t sec t
dT sent i cos t j; dt
dT dt
sent
2
cos t 1
N
T '(t) sent i cos t j sent i cos t j T '(t) 1
T '(t) 1 cos t r '(t) sec t
2
2. r(t) ln sec t i tj, / 2 t / 2
14 | P á g i n a
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Solución
sec t tan t r '(t) i j tan t i j sec t r '(t) T
tan t
2
11 sec 2 t sec t sec t, / 2 t / 2
r(t) tan t 1 dT cos t i sent j i j sent i cos t j; r '(t) sec t sec t dt
dT dt
cos t
2
sent 1 N 2
T '(t) cos t i sent j; T '(t)
1 dT 1 1 cos t v dt sec t
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