2.3.1—Reciprocal trig functions

cosec x=1/sin x, sec x=1/cos x and cot x=1/tan x=cos x/sin x wherever the denominator is non-zero. Their graphs inherit zeros and asymptotes from the original functions.

Use reciprocal values rather than inventing new triangle rules. Mark undefined angles and use the original sine or cosine sign to determine the reciprocal sign.

sec(π/3)=2 because cos(π/3)=1/2; sec x is undefined where cos x=0.

cosec x is not sin⁻¹x, and reciprocal graphs do not cross the x-axis because a reciprocal cannot equal zero.