MATH PRECALCULUS

Question

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

x	0	2	4	6	8	10	12
y	-2	-6	-2	2	-2	-6	-2

Answer 1

Notice that the y-values range from -6 to +2. The average of those two extremes is -2 which we see repeated most often as the y-value. So let's try a sine or cosine function with centerline at -2 that has an amplitude of 4 (goes up to +2 and down to -6). We can see that it starts at 0 at the centerline and then goes down from there which would be indicative of a negative sine function. We can see that the period must be 8 since we have (2, -6) and then (10, -6). So the multiplier in front of the "x" must be 2π/8 or π/4.

So a function could be y = -4sin(π/4x) - 2