What is the curvature of this function?

Question

Seems like any answer I get is so big its like 2 pages of work. Dont know what is going on:

c(t) = i(sint)+j(sint)+k(5cost)

I know it's supposed to be ||dT/t||/||c'(t)||

Answer 1

c: r(t)=i(sint)+j(sint)+k(5cost)

k=| r' x r" | / | r' |³  

r'(t)=i(cost)+j(cost)+k(-5sint)

r"(t)=i(-sint)+j(-sint)+k(-5cost)

. . . . . | . i . . .j . . . k . .|

r' x r"=|cost cost -5sint |=

. . . . .|-sint -sint -5cost|

=i(-5cos²t-5sin²t)+

j(5sin²t+5cos²t)+

k(-sintcost+sintcost)

r' x r"= -5i+5j+0k

| r' x r" |=√[(-5)²+5²+0²]=5√2

| r' |=√[(cost)²+(cost)²+(-5sint)²]=

√(2cos²t+25sin²t)=√(2+23sin²t)

k=5√2/√(2+23sin²t)³