Math Problem Statement
ind parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t cos(t) text(, ) y = t^4 text(, ) z = t sin(t) text(; ) ( - pi text(, ) pi^4 text(, ) 0 ) x(t) = - pi - t y(t) =
Incorrect: Your answer is incorrect. z(t) =
Incorrect: Your answer is incorrect.
Illustrate by graphing both the curve and the tangent line on a common screen. (Do this on your graphing device. Your instructor may ask to see this graph.) Need Help? Read It
Solution
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Math Problem Analysis
Mathematical Concepts
Parametric Equations
Calculus
Derivatives
Tangent Line
Formulas
x(t) = t cos(t)
y(t) = t^4
z(t) = t sin(t)
dx/dt = cos(t) - t sin(t)
dy/dt = 4t^3
dz/dt = sin(t) + t cos(t)
Parametric equation of tangent line: x(t) = x_0 + t dx/dt, y(t) = y_0 + t dy/dt, z(t) = z_0 + t dz/dt
Theorems
Derivative Theorem for Parametric Curves
Tangent Line Equation
Suitable Grade Level
College Level (Calculus I or II)
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