Pre calc. amplitude,period, phase shift and endpoint?

Question

How do you solve this need help asap, thank you!!

Find amplitude,period, phase shift and endpoint

1). y= cos 2( x- (pie/2)

2). y= 2sin (1/2)x - (pie/6)

Answer 1

OK small pet peeve, it's PI not PIE the Greek letter not the delicious baked pastry.

y=a*sin(b(x-c)+d

y=a*cos(b(x-c)+d

Amplitude=|a| (if a is negative the function flips around the x-axis)

Period=2pi/b

Phase Shift=-c/b (the negative in the function above is part of the function if it is x-c, c is positive if it is x+c, c is negative...WATCH the signs)

Vertical Shift=d

to find the endpoints solve: 0≤bx-c≤2pi then put the x-values into the function to find the y-values

1. Amp=1, Per=2pi/2=pi, Phase shift= -(pi/2)/2=-pi,

endpoints:0≤1x-pi/2≤2pi or pi≤x≤3pi

(pi,-1), (3pi,-1)

2.Amp=2, Per=2pi/(1/2) = 4pi, Phase Shift=0,

endpoints=0≤1/2x≤2pi or 0≤x≤4pi

(0,-pi/6), (4pi,-pi/6)

Source(s): http://www.cedarvalleycollege.edu/FutureStudents/S... http://education.tjc.edu/math/Comp_009/comp_009.3....