Suppose the vector-valued function r(t) = (f(t), g(t), h(t)) is smooth on an interval containing the point

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Suppose the vector-valued function r(t) = (f(t), g(t), h(t)) is smooth on an interval containing the point t0. The line tangent to r(t) at t = t0 is the line parallel to the tangent vector r'(t0) that passes through (f(t0), g(t0), h(t0)). For each of the following functions, find an equation of the line tangent to the curve at t = t0. Choose an orientation for the line that is the same as the direction of r'.

r(t) = (2 + cos t, 3 + sin 2t, t); t0 = π/2

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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