What are the limits of arcsec(x) and arccsc(x) as x approaches negative and positive infinities?

2 Answers

• limit of arcsec(x) approaching infinity or negative infinity is pi/2

  limit of arccsc(x) approaching infinity or negative infinity is 0

• Since cos(PI/2) = 0, its reciprocal sec(PI/2) approaches infinity as x approaches pi/2

  lim x --> infinity arcsec(x) = PI/2

  Since sin(0) = 0, its reciprocal csc(0) approaches infinity as x approaches 0.

  lim x-->infinity arccsc(x) = 0