3.3.1—Reciprocal trig functions

cosec x=1/sin x, sec x=1/cos x and cot x=cos x/sin x. They are undefined where the denominator is zero and never equal zero themselves.

Use the original function’s sign and period to sketch reciprocal branches. Mark vertical asymptotes before plotting turning points.

sec x has asymptotes at π/2+nπ and reaches ±1 at x=nπ.

Reciprocal notation is not inverse-function notation: sec x is not cos⁻¹x.