Answer:
Amplitude = -4; period = π; phase shift: x = π/2
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 (phase 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.
* Now lets solve the problem
∵ f(x) = A sin (B(x + C)) + D
∵ f(x) = -4 sin (2x + π) - 5 ⇒ take 2 from the bract (2x + π) common factor
∴ f(x) = -4 sin 2(x + π/2) - 5
∴ A = 4 , B = 2 , C = π/2 , D = -5
∵ A is the amplitude
∴ The amplitude is -4
∵ The period is 2π/B
∴ The period = 2π/2 = π
∵ C is the horizontal shift (phase shift)
∴ The phase shift π/2 (to the left)
* Amplitude = -4; period = π; phase shift: x = π/2
