Acepheid variable star is a star whose brightness alternately increases and decreases. suppose that cephei joe is a star for which the interval between times of maximum brightness is 5.1 days. its average brightness is 3.6 and the brightness changes by +/-0.55. using this data, we can construct a mathematical model for the brightness of cephei joe at time t, where t is measured in days:
b(t)=3.6+0.55sin(2pi(t)/5.1)

i found the rate of change.. it's
0.677598cos(1.232t)

but, i also need to find the rate of increase after one day. (correct to two decimal places)

can someone ?

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?