4.4/4.5 (Graphs of Trigonomic Functions) Flashcards
What does one period of the graph of y=sin x look like?
mid up mid down mid
What does one period of the graph of y=cos x look like?
up mid down mid up
Should there be more than the correct number of waves?
No
What does the “a” in y=a+b sin c(x-d) symbolize? How can you find this in terms of max and min? What direction does this go?
Vertical shift, found with (max+min)/2, goes up and down
What does the “b” in y=a+b sin c(x-d) symbolize? How can you find this in terms of max and min?
Amplitude change, found with (max-min)/2
Is amplitude always positive?
Yes
What does the “c” in y=a+b sin c(x-d) symbolize? How can you use this to find the period?
Period change, which calculates the period with 2π/c
What does the “d” in y=a+b sin c(x-d) symbolize? What direction does this go?
Phase shift, which goes left and right
What does one period of the graph y=tan x look like?
asy., down, mid, up, asy.
Is y=tan x centered about the y-axis?
Yes
What does the graph of y=cot x look like?
asy., up, mid, down, asy.
What does the graph of y=csc x look like?
asy., up para., asy., down para., asy.
What does the graph of y=sec x look like?
asy., up para., mid, down para., asy.
What is the period of tan x and cot x?
π
How is the graph of y=sec x compare to y=csc x?
sec x is csc x horizontally shifted left π/2
