For what values of θ between 0 ≤ θ ≤ 2π is the sine, secant and tangent function not defined?

Make a right triangle and label the sides. The side opposite the angle is labelled opposite side (b), the one adjacent
is the adjacent side (a) and the last is the hypotenuse (c).

• The sine of θ = b/c   Since the length of the hypotenuse side c can never equal 0 the sine function is defined for all angles.


• The secant of θ = c/a   Since the length of side "a" can equal 0 the secant function is not defined for all angles.
  Side "a" will equal 0 at π/2 and 3π/2 and hence the secant's graph has vertical asymptotes at those angles.


• The tangent of θ = b/a   Since the length of side "a" can equal 0 the tangent function is not defined for all angles.
  Side "a" will equal 0 at π/2 and 3π/2 and hence the tangent's graph has vertical asymptotes at those angles.

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