Question

Find the norm of vector r prime of t when r(t) = t^2i + 2sintj + 2costk

Answer 1

r'(t)=?

r(t) is given

Answer 2

so start with taking derivative

Answer 3

then square each component , add them

Answer 4

take square root

Answer 5

\[\sqrt(4t^2 + 4\cos^2t + 4\sin^2t)\]

Answer 6

What's the trig identity for cos and sin?

Answer 7

cos^2 t + sin^2 t =1

Answer 8

so does the second half of that just become 8?

Answer 9

4( 1)=4

Answer 10

Can you explain? I can never follow this one...

Answer 11

cos(t)^2+sin(t)^2=1

4(cos(t)^2+sin(t)^2)=4

Answer 12

Ohhhh.... Is that technically combining like terms?

Answer 13

I guess

Answer 14

Thanks!

Answer 15

no problem