Need answer asap! 50 pts! which of the following would best represent a sine function with an amplitude of 7, a period of pi over 4 , and a midline at y = 3? (1 point) f(x) = 7 sin 8x + 3 f(x) = 3 sin 8x + 7 f(x) = 7 sin( pi over 4 x) + 3 f(x) = 3 sin( pi over 4 x) + 7

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

step-by-step explanation:

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