Help peter not fail methods thread :P

[Mao]

,

[dcc]

Look at the first few solutions, try to establish a pattern:





Therefore, a general pattern seems to be:

[pete_owntbychem]

what does the k and the element Z represent?

[Mao]

k: a variable

Z: set of integers [similar to R, set of real numbers]


so, k is basically any integer.

[pete_owntbychem]

state the amplitudes and periods of

(a) y= sin(x/3)

(b) y= -4sin(x/2)

(c) y= 2sin(x/3)

(d) y= sinx

(e) y=3cosx

thanks!

[bucket]

the amplitude is always the constant in front of the expression.

ie.
a) has the amplitude of 1

b) has amplitude of -4

the period is found using the formula where is the number that x is multiplied by
ie.
a) , x is multiplied by , therefore the period is which is which is

[pete_owntbychem]

got it, thanks

[Rietie]

the amplitude is always the constant in front of the expression.

ie.
a) has the amplitude of 1

b) has amplitude of -4

the period is found using the formula where is the number that x is multiplied by
ie.
a) , x is multiplied by , therefore the period is which is which is

The amplitude is not negative or positive, it is simply the number (regardless of what sign is in front of it).

And don't forget that for tan graphs, the period is pi over n (while for sin and cos it is 2pi over n).

[polky]

2 - cosx is the same as -cosx + 2... apply your transformations!

- the negative sign in front of the cos means that the graph has been reflected about the x axis (all previous positive y values are now negative and vice versa)
- the +2 means that the graph has been translated vertically upwards by 2 units.  Which means that your range for the graph is now from [1,3]
 
(i'll let someone else do part b)

[Mao]

(b)
interpret it in terms of transformations:

1. shrink the sin graph down (x axis) to a third of its size (sin[3x])

2. expand it to twice its verticle size (2sin[3x])

3. invert it vertically (-2sin[3x])

4. move it up one (1-2sin[3x])

[Glockmeister]

Mao, its times like these that we need your tablet.