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Find the Unit Tangent Vector T(t)T ( t ) r(t)=⟨2sin⁡t,4t,2cos⁡t⟩\mathbf { r } ( t ) = \langle 2 \sin t , 4 t , 2 \cos t \rangle

Question 42

Multiple Choice

Find the unit tangent vector T(t) T ( t ) . r(t) =⟨2sin⁡t,4t,2cos⁡t⟩\mathbf { r } ( t ) = \langle 2 \sin t , 4 t , 2 \cos t \rangle


A) ⟨cos⁡t25,25,−sin⁡t25⟩\left\langle\frac { \cos t } { 2 \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , - \frac { \sin t } { 2 \sqrt { 5 } } \right\rangle
B) ⟨3cos⁡t,6,−3sin⁡t⟩\langle3 \cos t , 6 , - 3 \sin t \rangle
C) ⟨cos⁡t5,25,−sin⁡t5⟩\left\langle\frac { \cos t } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , - \frac { \sin t } { \sqrt { 5 } } \right\rangle
D) ⟨35cos⁡t,6,−35sin⁡t⟩\langle3 \sqrt { 5 } \cos t , 6 , - 3 \sqrt { 5 } \sin t \rangle
E) ⟨−cos⁡t25,425,3sin⁡t25⟩\left\langle- \frac { \cos t } { 2 \sqrt { 5 } } , \frac { 4 } { 2 \sqrt { 5 } } , \frac { 3 \sin t } { 2 \sqrt { 5 } } \right\rangle

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