Determine the amplitudo, the period , the phase shift and the midline of the function f(x) = (1/2)−sin ((1/2)x+(π/2))


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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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