trig and geometry

Question 1

how do you find the amplitude of a graph from given data

Answer 1

(max height - min height) / 2

Question 2

how do you find the period with given data

Answer 2

b = 2pi/period
or
b = 360/period

Question 3

how do you find the vertical change with given data

Answer 3

c = vertical change
c = (max height + min height) / 2

Question 4

what does a,b and c mean in this trig format :

a cos bt + c

Answer 4

a = amplitude
b = 2pi/period
c = vertical change

Question 5

A particle P, on the top of a spring which is fixed to a table, initially at its max height above the table of 0.5m. Its min height above the table occurs at 0.16m, 0.3 seconds later. Find a model in the form h = a cos bt + c for the height of P , above the table at t seconds

Answer 5

a = hmax - hmin /2
0.5 - 0.16/2 = 0.17

b = 2pi/period
period = 0.3 x 2 (time taken for ball to go down then up) = 0.6
2pi/0.6 = 10pi/3

c = max height + min height /2
0.5 + 0.16 /2 = 0.33

0.17 cos 10pi/3t +0.33