The trigonometric ratios can likewise be considered as features of a variable which is the measure of one angle.

This angle measure deserve to either be given in degrees or radians . Here, us will usage radians. Since any angle with a measure greater than 2 π radians or less than 0 is tantamount to some angle with measure 0 ≤ θ 2 π , all the trigonometric attributes are periodic .

The graph of the sine function looks choose this:

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note that the domain the the duty y = sin ( x ) ) is all real numbers (sine is defined for any type of angle measure), the variety is − 1 ≤ y ≤ 1 .

The graph that the cosine function looks prefer this:

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The domain of the duty y = cos ( x ) is all actual numbers (cosine is characterized for any angle measure), the selection is − 1 ≤ y ≤ 1 .

The graph that the tangent function looks choose this:

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The domain the the duty y = tan ( x ) ) is all actual numbers other than the worths where cos ( x ) is same to 0 , that is, the worths π 2 + π n for every integers n . The range of the tangent duty is all real numbers.

The graph of the secant duty looks like this:

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The domain the the role y = sec ( x ) = 1 cos ( x ) is again all actual numbers except the values where cos ( x ) is same to 0 , that is, the values π 2 + π n for all integers n . The variety of the duty is y ≤ − 1 or y ≥ 1 .

The graph the the cosecant role looks prefer this:

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The domain of the function y = csc ( x ) = 1 sin ( x ) is all actual numbers except the worths where sin ( x ) is equal to 0 , that is, the values π n for every integers n . The range of the function is y ≤ − 1 or y ≥ 1 .

The graph of the cotangent function looks favor this:

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The domain that the role y = cot ( x ) = cos ( x ) sin ( x ) is all genuine numbers except the worths where sin ( x ) is same to 0 , that is, the worths π n for every integers n .


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The variety of the function is all genuine numbers.