Determine-the-amplitudo-the-period-the-phase-shift-and-the-midline-of-the-function-f-x-1-2-sin-1-2-x-pi-2-

Question Number 125993 by bramlexs22 last updated on 16/Dec/20

D e t e r m i n e t h e a m p l i t u d o, t h e

p e r i o d, t h e p h a s e s h i f t a n d t h e

m i d l i n e o f t h e f u n c t i o n

f (x) = \frac{1}{2} - \sin (\frac{1}{2} x + \frac{π}{2})

Answered by liberty last updated on 16/Dec/20

F o r t h e f u n c t i o n f (x) = A \sin (B (x - \frac{C}{B})) + D

t h e a m p l i t u d e i s ∣ A ∣, t h e p e r i o d i s ∣ \frac{2 π}{B} ∣, t h e

p h a s e s h i f t i s \frac{C}{B} a n d t h e m i d l i n e i s y = D .

c o n s i d e r f (x) = \frac{1}{2} - \sin (\frac{1}{2} x + \frac{π}{2}) o r

f (x) = - \sin (\frac{1}{2} (x - (- π))) + \frac{1}{2}

g i v e s w e {\begin{cases} a m p l i t u d e a s ∣ - 1 ∣= 1 \\ t h e p e r i o d a s ∣ \frac{2 π}{1 / 2} ∣ = 4 π \\ t h e p h a s e s h i f t a s - π \\ t h e m i d l i n e a s y = \frac{1}{2} \end{cases}

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