6.1-6.2 Notes

length of one complete cycle

period

What is the period of y = sin(x) function?

2π, or 360 degrees

horizontal center line, halfway between the maxima and minima

midline

What is the midline of a y = sin(x) function?

y = 0

distance between the midline and a maximum or minimum (the height of the wave).

amplitude

What is the amplitude of a y = sin(x) function?

1

What is the period of y = cos(x)?

2π

What is the midline of y = cos(x)?

y = 0

What is the amplitude of y = cos(x)?

1

horizontal shift for a trig function

phase shift

sin(x + π/2 )

π/2 to the left (remember, + for a horizontal shift moves to the left)

A function f(x) is odd if…

It is symmetric over the origin

­f(-x) = -f(x)

odd function

A function f(x) is even if…

­It is symmetric over the y-axis

f(-x) = f(x)

even function

Is y = sin(x) even or odd?

odd

Is y = cos(x) even or odd?

even

What is the order of type of points for a sine graph?

intercept, max, intercept, min, intercept

What is the order of type of points for a cosine graph?

max, intercept, min, intercept, max

distance between points

step size

What is the step size for a parent function?

π/2

How do you find the step size generally?

period/4

What is the A in a y = AsinBx function?

amplitude

We always consider the amplitude to be ________.

positive

If A is negative, we will…

reflect the function over the x-axis.

What is the B in a y = AsinBx function?

horizontal scale factor

What does B affect in a y = AsinBx function?

the period of the function

The period of the function will be…

2π/B

Write out the general form of a sine function:

y = Asin(B(x-C)) + D

What is A in y = Asin(B(x-C)) + D?

amplitude

What is the period in y = Asin(B(x-C)) + D?

2π/B

What is the C in y = Asin(B(x-C)) + D?

phase shift (must be factored out)

What is the D in y = Asin(B(x-C)) + D?

vertical shift (midline is at y = D)

What do you do if there is a phase shift?

You would have it as the first X coordinate. (0 + phase shift)

What is the order of key points of a sine function if it is negative?

intercept, min, intercept, max, intercept

How do you find the maximum?

midline + amplitude

How do you find the minimum?

midline - amplitude

What is the order of key points of a cosine function if it is negative?

min, intercept, max, intercept, min

What are the x-intercepts of a y = sin(x) parent function graph?

x = 0 + πk, k ∈ z

What is the maxima of a y = sin(x) parent function graph?

x = π/2 + 2πk, k ∈ z

What is the minima of a y = sin(x) parent function graph?

x = 3π/2 + 2πk, k ∈ z

What are the x-intercepts of a y = cos(x) parent function graph?

x = π/2 + πk, k ∈ z

What is the maxima of a y = cos(x) parent function graph?

x = 0 + 2πk, k ∈ z

What is the minima of a y = cos(x) parent function graph?

x = π + 2πk, k ∈ z

Equation of maxima for y = sin(x)

y = first max + periodk

Equation of intercept for y = sin(x)

y = 0 + first interceptk

Equation of minima for y = sin(x)

y = first min + periodk

Equation of maxima for y = cos(x)

y = first max + periodk

Equation of minima for y = cos(x)

y = 0 + periodk

Equation of intercept for y = cos(x)

y = first intercept + periodk

What is the domain of a y = sin(x) function?

(-∞, ∞)

What is the range of a y = sin(x) function?

\[min, max\]