6.3 Notes

What is sin parallel?

csc

What is cos parallel?

sec

Csc & Sec: Between the vertical asymptotes, flip the curves __________.

upside down

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

2π

What is the domain of the y = csc(x) parent function?

{x | x ≠ 0 + πk}, where k is any integer

What is the range of the y = csc(x) parent function?

(-∞, -1\] U \[1, ∞)

Is y = csc(x) even or odd?

odd

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

2π

What is the domain of the y = sec(x) parent function?

{x | x ≠ π/2 + πk}, where k is any integer

What is the range of the y = sec(x) parent function?

(-∞, -1\] U \[1, ∞)

Is y = sec(x) even or odd?

even

What is the order of type of points for a y = csc(x) graph?

int, max, int, min, int

What does a y = csc(x) graph look like?

The y = csc(x) graph is the one with the x shapes. At every min and max, you draw a sort of arrow looking structure that either goes up or down. It looks like a sine, and it has vertical asymptotes at the intercepts.

What is the order of type of points for a y = sec(x) graph?

max, int, min, int, max

What does a y = sec(x) graph look like?

The y = sec(x) graph is the one with the x shapes. At every min and max, you draw a sort of arrow looking structure that either goes up or down. It looks like a cosine, and it has vertical asymptotes at the intercepts.

The vertical asymptotes in a y = csc(x) graph are the same as…

the intercepts

How do you find the period in y = csc(x) and y = sec(x)?

2π/B

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

π

What is the vertical asymptote of the y = tan(x) parent function?

x = π/2 +πk, where k is any integer

What is the domain of the y = tan(x) parent function?

{x | x ≠ π/2 + πk, k ∈ z}

What is the range of the y = tan(x) parent function?

all real numbers

Is y = tan(x) even or odd?

odd

What is the general form of a y = tan(x) function?

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

What does A represent in y = Atan/cot(B(x - C)) + D?

A determines the vertical stretch and reflection (+ or - ), though we don’t call it the amplitude

How do you find the period in y = tan(x) and y = cot(x)?

π/B

Step size is always going to be…

period/4

What is the order of type of points for a y = tan(x) graph?

int, high point, vertical asymptote, low point, int

What would be the y coordinate if it is a vertical asymptote point?

und

What is the order of type of points for a y = tan(x) graph if it was reflected?

int, low point, vertical asymptote, high point, int

Where do tangent functions have asymptotes?

x = 1/2Period + Periodk, where k is any integer

What do y = tan(x) graphs look like?

There are three sections of this graph. In the middle, it has a full up arrow and down arrow. In the left section, it only has the up part. In the right section, it only has the down part. There are vertical asymptotes one away from the origin.

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

π

What is the vertical asymptote of the y = cot(x) parent function?

x = 0 + πk, k is any integer

What is the domain of the y = cot(x) parent function?

{x | x ≠ 0 + πk, k ∈ Z}

What is the range of the y = cot(x) parent function?

all real numbers

Is y = cot(x) even or odd?

odd

What is the order of type of points for a y = cot(x) graph?

asymptote, high point, intercept, low point, asymptote

What is the order of type of points for a y = cot(x) graph if it was reflected?

asymptote, low point, intercept, high point, asymptote

Where do cotangents have asymptotes?

x = 0 + Periodk, where k is any integer

What do y = cot(x) graphs look like?

There are asymptotes three points away from the origin. There are two sections, which are identical to one another. It looks like a dance move, kinda.

Don’t forget to put the ___________ on sec and csc graphs.

arrows