Question

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

Answer 1

Answer:

  y = 3 -5sin((π/2)x)

Step-by-step explanation:

We notice the function is periodic with a period between minima of (5-1)=4. It has a maximum of 8 and a minimum of -2, so for the form ...

  y = Asin(kx) +C

the value of A is ...

  A = (1/2)(8 -(-2)) = 5

and the value of C is ...

  C = (1/2)(8 +(-2)) = 3

The function is at its middle position (3) at x=0, and is headed downward toward -2 at x=1, so can be modeled by the opposite of the sine function. That is, an appropriate value for A is -5.

The value of k is ...

  k = 2π/period = 2π/4 = π/2

Then the possible formula for the function is ...

  y = -5sin((π/2)x) +3