When starting with acceleration to get to velocity, we have to think about what gives us out a derivative of sine or negative sine if we want, and that's going to be cosine. So the cosine 3T would give us out negative sine. But then by the chain rule we have to divide by the derivative of the inside. So the derivative of that 3T is 3. So the 9 / 3 would give us 3 cosine 3T plus C1. Now they gave us an initial velocity point of V naughty or V0 equaling 3. So three goes in for our V and zero goes in for our T so we get 3 equaling 3 cosine 3 * 0 cosine of 0 is 1, so 3 * 1. So we can see that C1 has to be 0, so our velocity is going to be 3 cosine 3T. Now to get our distance we want to think about what gives us out cosine as a derivative, and that'd be sine the 3T. We need them to take by the chain rule the derivative of 3T and divide it. Because we're undoing the derivative, we're trying to find the anti derivative. Those threes would then cancel and we get sine 3T plus C2, some new constant equaling S. Given our zero and our -7, we're going to put -7 in for the S and 0 in for the T. Sine of 0 is 0, so we can see C2 has got to be -7. So S equals sine three t -, 7.