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Unit Tangent Vector Calculator

Find unit tangent vectors step by step

The calculator will find the unit tangent vector to the vector-valued function at the given point, with steps shown.

Related calculators: Unit Normal Vector Calculator, Unit Binormal Vector Calculator

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Your Input

Find the unit tangent vector for r⃗(t)=⟨2sin⁡(t),2cos⁡(t),7⟩\mathbf{\vec{r}\left(t\right)} = \left\langle 2 \sin{\left(t \right)}, 2 \cos{\left(t \right)}, 7\right\rangle.

Solution

To find the unit tangent vector, we need to find the derivative of r⃗(t)\mathbf{\vec{r}\left(t\right)} (the tangent vector) and then normalize it (find the unit vector).

r⃗′(t)=⟨2cos⁡(t),−2sin⁡(t),0⟩\mathbf{\vec{r}^{\prime}\left(t\right)} = \left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle (for steps, see derivative calculator).

Find the unit vector: T⃗(t)=⟨cos⁡(t),−sin⁡(t),0⟩\mathbf{\vec{T}\left(t\right)} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangle (for steps, see unit vector calculator).

Answer

The unit tangent vector is T⃗(t)=⟨cos⁡(t),−sin⁡(t),0⟩\mathbf{\vec{T}\left(t\right)} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangleA.