Characteristics of Tangent and Cotangent function
y-intercept of y=tan x
0
How many halfway points are there for each cycle in the tan function? What is the y-coordinate of the halfway point to the left? What is the y-coordinate of the halfway point to the right?
2; -1; 1
How many halfway points are there in the cot function? What is the y-coordinate of the halfway pint to the left? To the right?
2; 1; -1
domain of y=cot x
All real numbers except integer multiples of π
domain of y= tan x
All real numbers except odd integer multiples of π/2
Which one of the two functions is one-to-one?
Both
period of y=cot x
P=π
range of y= tan x
(-∞,∞)
range of y=cot x
(-∞,∞)
In the tan function, the x-coordinates of the center points are also the (complete the sentence)
x-intercepts, or zeros, and are of the form nπ where n is an integer
In the cot function, the center points are also the (complete the sentence)
x-intercepts, or zeros, and are of the form x=(2n+1)π/2 where n is an integer
The tan function has infinitely many vertical asymptotes with equations (complete sentence)
x= (2n+1)π/2
The cot function has infinitely many vertical asymptotes with equations (complete the sentence)
x=nπ where n is an integer
period of y= tan x
π
Is the graph even or odd; is the graph symmetric about the origin or about the y-axis?
odd; about the origin
Is the tan function even or odd? Is the graph symmetric about the origin or about the y-axis?
odd; symmetric about the origin