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Chapter 11: Q. 38 (page 860)

Evaluate and simplify the indicated quantities in Exercises 35–41.
$t (\sin t, \cos t)$

Short Answer

Expert verified

The simplification of $t (\sin t, \cos t)$ is $(t \sin t, t \cos t)$ .

Step by step solution

Step 1. Given Information.

The quantities:

$t (\sin t, \cos t)$

Step 2. Multiply the scalar with function.

Multiply the scalar with the vector function,

$t (\sin t, \cos t) = (t \sin t, t \cos t)$

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Most popular questions from this chapter

Let $r (t) = (x (t), y (t), z (t)), t \in [a, \infty),$ be a vector-valued function, where a is a real number. Explain why the graph of r may or may not be contained in some sphere centered at the origin. (Hint: Consider the functions $r_{1} (t) = (\cos t, \sin t, 1 / t)$ and $r_{2} (t) = (\cos t, \sin t, t), both with domain [1, \infty) .)$

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Prove that the tangent vector is always orthogonal to the position vector for the vector-valued function.

$r (t) = <\sin t, \sin t \cos t, \cos^{2} t>$

$Complete the following definition : If r (t) = <x (t), y (t), z (t)> is a differentiable position function, then the velocity vector v (t) is . . . .$

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Evaluate and simplify the indicated quantities in Exercises 35–41.t(sint,cost)

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Multiply the scalar with function.

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Most popular questions from this chapter

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Evaluate and simplify the indicated quantities in Exercises 35–41.
$t (\sin t, \cos t)$