Answer:
Explanation:
a) A = (28 - 14) / 2 = 7
b) T = 2(11½ - 6½) = 10
c) P = (6½ - T/4, 28 - A) = (4, 21)
d) general form y = Asin(ωx + φ) + d
We have already found amplitude A = 7
the upward displacement from the x axis is 21
The portion in parenthesis will be in radians. The cycle repeats every 10 x units so ω = 2πx/10 = 0.2πx
To find φ, which is 4/10 of a cycle behind the upward tracing zero point, we subtract 2π(4/10) = 0.8π
y = 7sin(0.2πx - 0.8π) + 21
y = 7sin(π(0.2x - 0.8)) + 21
e) The easiest "difference" we can make is to change φ
Because the pattern repeats, 4/10 of a cycle backward is the same as 6/10 of a cycle forward. 6/10(2π) = 1.2π
y = 7sin(π(0.2x + 1.2)) + 21
We could also change it to a cosine function which would also change our option for φ by π/2