Trigonometric Functions 4.6 Graphs of Other Trigonometric Functions csc, sec, tan, & cot Graphing csc and sec is done by graphing its reciprocal function first.

v.s. = A = P = h.s. = 3 2 Graph y = 3 + 2 csc + sin x 5 3 1 x-axis Find the midpoint to locate y-axis. Draw vert. asy.

What is the range and domain of y? Domain: To find the domain of csc x , set what comes after csc =

v.s = 2 h.s. = y = 2 – 4 sec (4x - ) y = 2 – 4 sec 4(x - ) P = A = 4 6 2 x-axis -2

Range: To find the domain, set what comes after sec =

y = - tan x y = tan x Range: 1 Domain: set whatever is after the tan = -1

y = -3 tan 2x Plug in –1, 0 and 1 for k to find vertical asymptotes. v.a.’s at Range:

y = cot x Range: Domain: set whatever is after the cot = Plug in -1, 0, and 1 for k to find the v.a.’s Period

Extra Sinusoid