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Domain and Range for Sec, Cosec and Cot Functions sec x will not be defined at the points where cos x is 0. Hence, the domain of sec x will be R-(2n+1)π/2, where n∈I. The range of sec x will be R- (-1,1).

The domain of the secant function excludes π2+kπ π 2 + k π for all integers k; these are the values where the denominator of the secant function (the cosine) is 0. The range of the secant function is the set of all real numbers with size greater than or equal to 1.

The correct answer is (–∞, –1 ] υ [ 1, ∞).

1 Answer. The range of secx is (−∞,−1]∪[1,∞).

Secant is an even function. The secant of an angle is the same as the secant of its opposite. So if the secant of anglet t is 2, the secant of−t − t is also 2.

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

The domain of a function is the specific set of values that the independent variable in a function can take on. The range is the resulting values that the dependant variable can have as x varies throughout the domain.

As with tangent and cotangent, the graph of secant has asymptotes. This is because secant is defined as. The cosine graph crosses the x-axis on the interval. at two places, so the secant graph has two asymptotes, which divide the period interval into three smaller sections.

Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

The domain of the function y=sec(x)=1cos(x) is again all real numbers except the values where cos(x) is equal to 0, that is, the values π2+πn for all integers n. The range of the function is y≤−1 or y≥1.

We may consider [0, π] as range of y = sec ^{–} ^{1} ( x ).

The graph of y = secx has vertical asymptotes at x =π2+nπ, where n is any integer.

We can determine whether each of the other basic trigonometric functions is even, odd, or neither, with just these two facts and the reciprocal identities. Thus tangent takes the form f(− x )=−f( x ), so tangent is an odd function.

The domain of the inverse tangent function is (−∞,∞) and the range is (−π2,π2). The inverse of the tangent function will yield values in the 1 st and 4th quadrants. Graphs of Inverse Trigonometric Functions.

Function | Domain | Range |
---|---|---|

sec − 1 ( x ) | (−∞,− 1 ]∪[ 1,∞) | [0,π2)∪(π2,π] |

csc− 1 ( x ) | (−∞,− 1 ]∪[ 1,∞) | [−π2,0)∪(0,π2] |

Trigonometric Functions

Function | Domain | Range |
---|---|---|

f ( x ) = cos ( x ) | (-∞, + ∞) | [-1, 1] |

f ( x ) = tan ( x ) | All real numbers except π/2 + n*π | (-in, + ∞) |

f ( x ) = sec ( x ) | All real numbers except π/2 + n*π | (-∞, -1] U [1, + ∞) |

f ( x ) = csc ( x ) | All real numbers except n*π | (-∞, -1] U [1, + ∞) |

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