Graphs of sec, csc and cot

Part of the Graphs of Trig Functions section of Coddy's Trigonometry journey. Lesson 38 of 51.

sec(x) = 1/cos(x). Where the cosine is 1 or −1 the secant is the same; where the cosine shrinks towards 0 the secant grows without limit; where the cosine is 0 there is an asymptote. The graph is a row of U shapes, opening up above the cosine's tops and down below its bottoms, and it never takes a value between −1 and 1.

$y = sec x as U shapes touching the dashed cosine at its tops and bottoms$

csc(x) = 1/sin(x) does the same to the sine: U shapes at its tops and bottoms, asymptotes where the sine is 0, at every multiple of π. Both have period 2π.

$y = cot x with falling branches and asymptotes at multiples of π, beside the dashed tangent$

cot(x) = cos(x)/sin(x) has its asymptotes where the sine is 0, at multiples of π, its zeros where the cosine is 0, at π/2 + kπ, and falling branches with period π.