Find a tangent vector at the indicated value of t. r(t) = ti + sin(5t)j + cos(6t)k; t = √6
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Step 1
Step 1: Calculate the derivative of r(t) with respect to t: \[ \frac{dr}{dt} = \frac{d}{dt} (ti + \sin(5t)j + \cos(6t)k) \] \[ = \frac{d}{dt} (t)i + \frac{d}{dt} (\sin(5t))j + \frac{d}{dt} (\cos(6t))k \] \[ = 1i + 5\cos(5t)j - 6\sin(6t)k \] Show more…
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