What is the domain and range of this: f(x)=sec((pie*x)/4)?-Collection of common programming errors

• I’m going to assume you mean “pi” and not “pie”, because I don’t know how to take the secant of a round, baked dessert. sec is the secant function. If you don’t know your six trigonometry functions, then I don’t know how you could answer this.

  f(x) = sec(π x / 4) = 1 / cos(π x / 4), so this is undefined when cos(π x / 4) = 0. Since cos(π/2), cos(3π/2), etc. = 0, this means the function is undefined for x = ±1, ±3, ±5, ±7… So the domain is “all real numbers except the odd integers”.

• You did not mention that this is a real function, but I a considering it as a real function: sec((pie*x)/4) = 1/(cos((pie*x)/4)) value of cosA is 0 when A is = (2n+1)(pie/2) hence (pie*x)/4 != (2n+1)(pie/2) x/2 != (2n+1) x != 2(2n+1) therefore the domain of f(x) is oll real nos except the doubles of odd numbers: D f(x) = R – {2(2n+1) : n is an integer} R f(x) = R – (-1,1) Note: Range of sec(x) is always from minus infinity to minus one and from plus one to plus infinity. As for “sec” it is just a function of the angle and equivalent to the ratio = hypotenuse/(adjacent sid of the angle)

  (in a right angle triangle.)

Originally posted 2013-11-09 21:07:42.