Find the Unit Tangent Vector T(t) to the Curve R $\langle \sin t , t , \cos t \rangle$

question 25

Multiple Choice

Find the unit tangent vector T(t) to the curve r (t) = $\langle \sin t , t , \cos t \rangle$ when t = 0.

• A) \(( - 1,0,0 )\)
• B) \(( 0,0 , - 1 )\)
• C) \(( 1,0,0 )\)
• D) \(( 0,0,1 )\)
• E) \(\left( 0 , \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } \right)\)
• F) \(\left( \frac { 1 } { \sqrt { 2 } } , 0 , \frac { 1 } { \sqrt { 2 } } \right)\)
• G) \(\left( \frac { 1 } { \sqrt { 2 } } , \frac { 1 } { \sqrt { 2 } } , 0 \right)\)
• H) \(\left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } \right)\)

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Definitions:

Coefficient of Determination

This indicates the proportion of the variation in the dependent variable that can be explained by the independent variable(s) in a regression model, quantifying the predictive power of the model.

Units

Basic quantities or measurements used to express and compare physical quantities.

Sample Size

Refers to the number of observations or data points collected in a study or used in statistical analysis.

Symbols

Characters or marks that are used to represent objects, quantities, or relations in mathematical expressions, equations, or in general notation.