Find a possible formula for the trigonometric function whose values are in the following table.

Question

Find a possible formula for the trigonometric function whose values are in the following table.

x	0	1	2	3	4	5	6
y	1	-5	1	7	1	-5	1

.

Answer 1

Try to find a function of the form y = Asin(Bx) + C, where lAl is the amplitude, period = 2π/B and the vertical shift = C.

The y-values vary from -5 to 7. 7 - (-5) = 12. Amplitude = 12/2 = 6 = lAl. Since the y-coordinate at 0 is on the midline and the y-coordinate at 1 is at the minimum, the sine graph is inverted. So, A = -6.

Midline = (-5+7)/2 = 1 = C

The y-value -5 repeats every 4 units. Period = 4 = 2π/B. So, B = π/2.

Therefore, y = -6sin(π/2 x) + 1 is a sine graph that passes through the given points.

Answer 2

y = -6sin(xπ / 2) + 1

Answer 3

y = 6sin[(3π/2)x] + 1