Question

Graph two full periods, highlighting the first period using bold marking and analyze each function.Y = 2 sin (1/2 (x + pi/2) ) + 1

Answer 1

Given

`y=2\sin((1)/(2)(x+(\pi)/(2)))+1`

Procedure

Period: 4pi

Interval length: In the graph 2 periods 8pi

Phase shift: -pi/2

1st Per. begins: -pi/2

1st Per. ends: 7pi/2

Amplitude: 2

Domain:

(-∞, ∞)

Range:

[-1,3]

y-intercep:

(0,2.414)

x-intercept:

`x=(11\pi)/(6)+4\pi n,(19\pi)/(6)+4\pi n,\text{ for any integer of n }`