What is the range of csc(pi/3 x+pi) ?

The range of csc(pi/3 x+pi) is f(x) = 1

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range of csc(pi/3 x+pi)

range

csc (\frac{π}{3} x + π)

f (x) \leq - 1 or f (x) \geq 1

Interval Notation

(- \infty, - 1] \cup [1, \infty)

Solution steps

The range of the basic

csc

function is

csc (\frac{π}{3} x + π) \leq - 1 or csc (\frac{π}{3} x + π) \geq 1

csc (\frac{π}{3} x + π) \leq - 1 or csc (\frac{π}{3} x + π) \geq 1

Therefore the range is

f (x) \leq - 1 or f (x) \geq 1

What is the range of csc(pi/3 x+pi) ?
The range of csc(pi/3 x+pi) is f(x)<=-1\lor f(x)>= 1