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

$y=2\sin(\frac{1}{2}(x+\frac{\pi}{2}))+1$

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:

$x=\frac{11\pi}{6}+4\pi n,\frac{19\pi}{6}+4\pi n,\text{ for any integer of n }$