Sine Function Problem

Question

a sine function has an amplitude of 4/7, period of 2pi, horizontal shift of -3pi, and a vertical shift of 1.

what is the y-value of the positive function at x=pi/2?

Answer 1

Here is the key to building the function:

The A = 4/7

Since the period (T) = 2π/B then B = 2π/T = 2π/2π = 1

C = -3π

D = 1

So the function is f(x) = 4/7sin[1(x- -3π] + 1 or

f(x) = 4/7sin(x + 3π) + 1

To find the y-value, just plug in π/2 into the function

f(π/2) = 4/7sin(π/2 + 3π) + 1

Since the period of sine is 2π, we can subtract 2π from the 3π horizontal shift without making a difference (the function repeats every 2π. So its easier if we use:

f(π/2) = 4/7sin(π/2 + π) + 1 which simplifies to:

f(π/2) = 4/7sin(3π/2) + 1

The sin(3π/2) = -1 so

f(π/2) = 4/7(-1) + 1 = -4/7 + 1 = 3/7

Answer 2

y = a·sin(b(x-c)) + d

1. a = amplitude = 4/7
2. b = 2π/period = 2π/2π = 1
3. c = horizontal shift = -3π
4. d = vertical shift = 1

y = a·sin(b(x-c)) + d

y = (4/7) sin(1(x-(-3π)) + 1

y = (4/7)sin(x + 3π) + 1

Plug in x = π/2 and use your calculator to get the answer.