tan cot csc sec characteristics

tan domain

all except (2n+1)π/2

tan range

(-∞,∞)

tan period

π

tan principal cycle

(-π/2,π/2)

tan vertical asym

x = (2n+1) π/2

tan y int

0

tan center pt, zero, x int

x = nπ

tan halfway pt y int

y = -1 (left)

y = 1 (right)

tan odd/even

odd

cot domain

all except nπ

cot range

(-∞,∞)

cot period

π

cot principal cycle

(0,π)

cot vertical asymptotes

x = nπ

cot y int

none

cot center point x int zeros

x = (2n+1)π/2

cot halfway pts y int

y=1 (left)

y=-1 (right)

cot even/odd

odd

csc domain

all but nπ

csc range

(-∞,-1] U [1,∞)

csc period

2π

csc vert asymp

x = nπ

csc rel max val of -1

x = 3π/2 + 2π

csc min value of 1

x = π/2 + 2πn

csc odd/even

odd

sec domain

all except (2n+1)π/2

sec range

(-∞,-1]U[1,∞)

sec period

2π

sec verti asymp

x = (2n+1)π/2

sec rel max -1

x = (2n+1)π

sec rel min value 1

x = 2πn

sec even/odd

even