Trigonometry functions

Question

Find a possible formula for trigonometric functions whose values are

X = 0,4,8,12,16,20,24

Y = -3,-9,-3,3,-3,-9,-3

Answer 1

Smallest y-value = -9 and largest = 3. So, Midline is y = [(-9) + 3]/2 = -3

Amplitude = half the distance from the largest value of y to the smallest = 6

Period = 20 - 4 = 16 Period = 2π/B = 16. So B = π/8.

Equation is y = -6sin[(π/8)x] - 3 Note: -6 because sine wave is inverted starting ar (0,-3)