Parent function graphing rules and stuff chapter 4 Pre Calc

All real numbers

Domain of sine

\[-1,1\]

Range of sine

Origin

Symmetry of sine

Odd

Sine odd or even?

Starts at the origin

Sine starting point

Starts at the maximum

Cosine starting point

All real numbers

Domain of cosine

\[-1,1\]

Range of cosine

y-axis

Symmetry of cosine

Even

Cosine odd or even?

all real numbers, x can’t = pi/2 +npi

Domain of tangent

all real numbers

Range of tangent

x=pi/2 +(or -) npi

Vertical asymptote (tan)

(npi, 0) (all integer multiples of x where sinx=0)

x-intercepts (tan)

(0,0)

y-intercept (tan)

origin

tangent symmetry

odd

tangent odd or even?

all real numbers x not = npi

Domain (cot)

All real numbers

range of cot

x = npi

vertical asymptote (cot)

(pi/2 + npi, 0)

x - intercepts (cot)

origin

cot symmetry

odd

cot odd or even?

All real numbers x not = npi

domain csc

(-infinity,-1\] u \[1, infinity)

range csc

x = npi

vertical asymptote csc

origin

csc symmetry

odd

csc odd or even

All real numbers x can’t = pi/2 + npi

sec domain

(-infinity, -1\] u \[ 1,infinity)

sec range

x = pi/2 + n

sec vertical asymptote