Primitive Function 3(sin(3t) + cos(3t))

[Attis]

Homework Statement

Find the primitive function s(t) for v(t)=3(sin(3t) + cos(3t)) for which s(0)=0

The Attempt at a Solution

v(t) =3(sin(3t) + cos(3t)) = 3sin3t +3cos3t

s(t) =cos3t -sin3t + C

0 = cos3(0) - sin3(0) + C
0= 1 + C
C=-1
such that my primitive function is cos3t - sin3t - 1

My teacher got another answer:
s(t) = -cos(3t) + sin(3t) + C
and s(0) = 0 = -1 + 0 + C such that C= 1 and the primitive function is sin3t -cos3t + 1

has he made a mistake? or am I confused?

 

[dirk_mec1]

You've made mistakes. What is the primitive function of cos and sin?

 

[Attis]

the primitive function is the anti-derivative. so cosx becomes sinx and sinx becomes -cosx?
s(t)=-cos3t+sin3t + C

Now I got it. I´d gotten confused between the derivative and the anti-derivative. Thanks for confirming that I´d made the mistake!