Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,433 questions

17,804 answers

1,438 comments

47,278 users

R(t) = acos^3(t) i + asin^3(t) j + k: Find derivative of vectors?

0 votes

I'm a bit stuck. The answer to this problem is:
-3asin(t)cos^2(t) i + 3asin^2(t)cost j

what I have is:
cos^3(t) - 3asin(t)cos^2(t) i + sin^3(t) + 3asin^2(t)cos(t) j

Please help. Much appreciated! :)

asked Mar 8, 2013 in CALCULUS by andrew Scholar

1 Answer

+1 vote

Differentiate  each side with respective t

R1 ( t ) = d/dt (a cos3(t) i + a sin3(t) j +k)

R1 ( t ) = d/dt (a cos3(t) i )+ d/dt ( a sin3(t) j ) + d/dt (k)

R1 ( t ) = a [ d/dt(cos3(t) i ] + a [ d/dt (sin3(t) j ] + 0

Recall : d/dt [cos3(A) ] = 3cos2(A) (-sin(A) ) and d/dt [sin3(A)] = 3Sin2(A) cos(A)

R1 ( t ) =  a [  3cos2(t) i (-sin ( t ) ) ( 1 ) ] + a [ 3(sin2(t) j (cos ( t ) (1)

R1 ( t ) = - 3asin(t) cos2(t) i  +3a sin2(t)cos(t) j

 

answered Mar 8, 2013 by diane Scholar

Related questions

asked Oct 31, 2017 in CALCULUS by anonymous
asked Jan 22, 2015 in CALCULUS by anonymous
asked Jan 22, 2015 in CALCULUS by anonymous
...