Equations for relationships

Question

x1 y1

0 55

15 35

30 10

45 35

60 55

75 35

90 10

105 35

120 55

Create two equations that describe the relationship, one using sin() and one using cos().

0-55 15-35 30-10.... the equation should be from x to f(x)

Answer 1

y = A cos B (x + C) + D

y = A sin B (x + C) + D

Period = 60, so B = 2∏ / 60 = ∏/30

Amplitude A = (max - min) /2 = (55-10)/2 = 22.5

D = A + min = 22.5 + 10 = 32.5

y = 22.5 cos ∏/30 x + 32.5

horizontal shift for sine function is 15. A quarter of the cycle

y = -22.5 sin (∏/30 x - 15) + 32.5