Very basic circuits 1 question. Charge and current

[A.J.710]

Homework Statement

Find the charge q(t) flowing through a device if the current is: 20 cos(10t + π/6)μA, q(0) = 2 μC

Homework Equations

∫ i(t)dt +q(0)

The Attempt at a Solution

I am studying for a test by working all the problems I can and then looking at the solutions manual. The solutions manual says the answer is (2sin(10t+π/6)+1)μC. I got the same thing except +2 at the end since q(0) is 2. It's really bugging me that I can't figure out why. Can anyone please explain?

 

[Doc Al]

The solutions manual says the answer is (2sin(10t+π/6)+1)μC. I got the same thing except +2 at the end since q(0) is 2.

If you plug in t = 0 to your solution and the manual's, which one gives the correct answer?

 

[A.J.710]

If you plug in t = 0 to your solution and the manual's, which one gives the correct answer?

Ahh, got it now. Thank you. I didn't realize that's what it meant. I was just adding the q(0) but I didn't realize until you pointed it out that the entire function in itself is q.