the signs of other trigonometric functions in different quadrants. In fact, we have the following table. I II III IV sin x – – cos x – – tan x – – cosec x – – sec x – – cot x – – . .
Domain and range of trigonometric functions From the definition of sine and cosine functions, we observe that they are defined for all real numbers. Further, we observe that for each real number x , – ≤ sin x ≤ and – ≤ cos x ≤ Thus, domain of y = sin x and y = cos x is the set of all real numbers and range is the interval [– , ], i.e., – ≤ y ≤ . TRIGONOMETRIC FUNCTIONS Since cosec x = sin x , the domain of y = cosec x is the set { x : x ∈ R and x ≠ n π , n ∈ Z } and range is the set { y : y ∈ R , y ≥ or y ≤ – }. Similarly, the domain of y = sec x is the set { x : x ∈ R and x ≠ ( n + ) π , n ∈ Z } and range is the set { y : y ∈ R , y ≤ – 1or y ≥ }.
The domain of y = tan x is the set { x : x ∈ R and x ≠ ( n + ) π , n ∈ Z } and range is the set of all real numbers. The domain of y = cot x is the set { x : x ∈ R and x ≠ n π , n ∈ Z } and the range is the set of all real numbers. We further observe that in the first quadrant, as x increases from to π , sin x increases from to , as x increases from π to π , sin x decreases from to . In the