Pre calc amplitude, phase shift, endpoint?

Question

How do you solve this?

Find the amplitude, period, phase shift and endpoint then graph the following functions.

1). y=cos2( x- (pie/2))

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

Answer 1

Favorite Answer

Okay, we just learned this in my class so hopefully I can explain this well enough.

This is the generic equation for both of sine and cosine: y= +or- a sin[+or- b(x-c)] + d. It is the same for cos except instead of sin it is cos.

The amplitude of the graph is the absolute value of a.

The period is 2pi/absolute value of b

The phase shift of the graph is c

The end behavior is determined by the leading coefficient so if a is - then the end behavior is -

For #1

amplitude= 1

period= pi

phase shift= -pi/2

end behavior= positive

Now see if you can do # 2 by yourself

Hope I helped :)

Answer 2

 

1.) Basic Cosine Function:

y = a Cos (bx - c) + d, where

Parameters:

Amplitude = a

Period = (2 / b) 'π'

Phase Shift = (- c / π) 'π'

y-intercept = d

y = Cos 2[x - (π/2)], or

y = Cos (2x - π)

a = 1

b = 2

c = π

d = 0

Amplitude = 1

¯¯¯¯¯¯¯¯¯¯¯

Period = π

¯¯¯¯¯¯¯¯¯

Phase = - 1

¯¯¯¯¯¯¯¯¯¯

2.) Basic Sine Function:

y = a Sin (bx - c) + d

Parameters are the same as in Problem 1 above, so

y = 2 Sin (0.5x - π/6)

a = 2

b = 0.5

c = π/6, or 0.524

d = 0

Amplitude = 2

¯¯¯¯¯¯¯¯¯¯¯¯

Period = 4π

¯¯¯¯¯¯¯¯¯¯

Phase = (- π/6) / π, or (- π/2) π

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

 

Source(s): 5/4/14