Trigonometric Functions

Where sin and cos intercept the x-axis, their reciprocal functions have ______________________.

Asymptotes

Graphs which intercept the x-axis/have asymptotes at odd multiples of pi/2:

Cos, sec, cot

y=tanx

Discontinuous, symmetric with origin X-intercepts at multiples of pi Asymptotes at ODD multiples of pi/2 Period of pi

y=cosx

Domain is all real numbers, range is 1<y<1 Period 2pi, x-intercepts at ODD multiples of pi/2 Continuous Symmetric with y-axis

y=sinx

Doman is all real numbers, range is -1<y<1 Period 2pi, x-intercepts at multiples of pi, continuous Symmetric with origin Crosses origin

Where sin and cos graphs have absolute maximums, the graphs of their reciprocal functions have relative ____________________________.

Minumums

Tan and cot are both symmetric along the __________________.

Origin

cos and sec cross and are symmetric with the y-axis, while sin and csc are symmetric with the ________________.

Origin

Which two trigonometric functions are continuous?

Sin and cos

y=cscx

Symmetric with origin No x-intercepts Discontinuous, asymptotes at multiples of pi

y=cotx

Symmetric with origin X-intercepts at ODD multiples of pi/2 Discontinuous, asymptotes at multiples of pi Period: pi

y=secx

Symmetric with y-axis No x-intercepts, only intercept at (0,1) Discontinuous, asymptotes at ODD multiples of pi/2

Two functions have no x-intercepts:

csc and sec

Each of the six Functions are _____________: they consist of repeating patterns

periodic

Sin, cos, csc and sec have periods of 2pi, while tan and cot have periods of ________, because the function of tan only goes halfway around the circle

pi

Graphs which intercept the x-axis/have asymptotes at multiples of pi:

sin, tan, csc