Previous year question papers

Range and Domain of trigonometric functions

The range of the trigonometric functions refers to the possible values that the function can output, while the domain refers to the possible input values that the function can accept.

Here are the diagrams of the range and domain of the six basic trigonometric functions:

1. Sine (sin)

• Range: [-1, 1]

• Domain: all real numbers

2. Cosine (cos)

• Range: [-1, 1]

• Domain: all real numbers

3. Tangent (tan)

• Range: all real numbers except for the special case of tan(90°)

• Domain: all real numbers except for the special case of tan(kπ), where k is an integer

4. Cotangent (cot)

• Range: all real numbers except for the special case of cot(90°)

• Domain: all real numbers except for the special case of cot(kπ), where k is an integer

5. Secant (sec)

• Range: all real numbers except for the special case of sec(90°)

• Domain: all real numbers except for the special case of sec(kπ), where k is an integer

6. Cosecant (csc)

• Range: all real numbers except for the special case of csc(90°)

• Domain: all real numbers except for the special case of csc(kπ), where k is an integer

Note: The special cases of tan, cot, sec, and csc at 90° and kπ occur because these functions are undefined at those points.