Find the domain of the vector-valued function r(t)=F(t)\timesG(t), where F(t)=\sin

Kelly Nelson

Kelly Nelson

Answered question

2021-12-08

Find the domain of the vector-valued function r(t)=F(t)×G(t), where F(t)=sinti+costj,G(t)=sintj+costk

Answer & Explanation

William Appel

William Appel

Beginner2021-12-09Added 44 answers

Step 1
It is given that F(t)=sinti+costj,G(t)=sintj+costk.
Step 2
Find the vector-valued function r(t)=F(t)×G(t)
r(t)=[ijksintcost00sintcost]
=(cos2t)i(costsint)j+(sin2t)k
The vector valued function is in the form of r(t)=f(t)i+g(t)j+h(t)k and the domain of the function is intersection of all that components.
Here, f(t)=cos2t,g(t)=costsint,h(t)=sin2t
It is observed that f(t)=cos2t,g(t)=costsint,h(t)=sin2tare defined everywhere.
Hence, the domain of r(t)is(,)

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