Answer:
f(x) = 7 sin 8x + 3 ⇒ 1st answer
Step-by-step explanation:
* Lets revise the trigonometry translation
- If the equation is y = A sin (B x + C) + D
* A is the amplitude
- The amplitude is the height from highest to lowest points and
divide the answer by 2
* The period is 2π/B
- The period is the distance from one peak to the next peak
* C is the horizontal shift
- The horizontal shift is how far the function is shifted to left
(C is positive) or to right (C is negative) from the original position.
* D is the vertical shift
- The vertical shift is how far the function is shifted vertically up
(D is positive) or down (D is negative) from the original position.
- The equation of the mid-line is y = D
* Now lets solve the problem
∵ f(x) = A sin(Bx + C) + D
∵ The amplitude is 7
∴ A = 7
∵ The period is 2π/B
∵ The period is π/4
∴ 2π/B = π/4 ⇒ divide both sides by π
∴ 2/B = 1/4 ⇒ Use cross multiplication
∴ B × 1 = 2 × 4
∴ B = 8
∵ The equation of the mid-line is y = D
∵ The equation of the mid-line is y = 3
∴ D = 3
- There is no mention for C
∴ C = 0
∴ f(x) = 7 sin 8x + 3
