# Thread: Differentiation of trig functions sin and cos

1. ## Differentiation of trig functions sin and cos

1 A particle is moving along a straight line so that, at a time t seconds after leaving a fixed point O, its velocity v ms-1 is given by V = 10sin ½ t.
a) Find the time when the acceleration, given by dv/dt , is first zero.
b) Find the velocity at this instant.

2. You're given the velocity function, so taking the derivative will give you the acceleration as a function of time.

The derivative of the sin(x) function is cos(x), but you must remember to apply the chain rule fur the inside function in this case.

Thus V' = acceleration = 10cos(t/2)*(1/2) = 5cos(t/2).

Then find the points where acceleration is equal to zero and solve for t. You can then plug in the appropriate value of t into the velocity function for part b.