Domain & Range of Trigonometric Functions
Using the table we can observe that Sin & Cos are defined for all real numbers. Further, we observe that for each real number x, – 1 ≤ sin x ≤ 1 and – 1 ≤ cos x ≤ 1.
Thus, domain of y = sin x and y = cos x is the set of all real numbers and range is the interval [– 1, 1 ], i. e., – 1 ≤ y ≤ 1.
Graph of Sin x & Cos x is shown. Both repeats after 2π
If we notice the graph of tan x, ire repeats after π. Thus domain of y = tan x is the set { x: x ∈ R and x ≠( 2n + 1) π / 2, n ∈ Z } and range is the set of all real numbers.