The trigonometric ratios can also be thought about as attributes of a change which is the measure up of one angle.

This edge measure can either be given in degrees or radians . Here, we will use radians. Since any type of angle v a measure higher than 2 π radians or much less than 0 is equivalent to some angle through measure 0 ≤ θ 2 π , every the trigonometric features are periodic .

The graph of the sine role looks favor this:

keep in mind that the domain the the duty y = sin ( x ) ) is all actual numbers (sine is identified for any kind of angle measure), the selection is − 1 ≤ y ≤ 1 .

The graph of the cosine duty looks favor this:

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

The graph of the tangent function looks choose this:

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

The graph of the secant function looks like this:

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

The graph of the cosecant duty looks prefer this:

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

The graph the the cotangent role looks choose this:

The domain of the role y = cot ( x ) = cos ( x ) sin ( x ) is all actual numbers other than the values where sin ( x ) is equal to 0 , that is, the values π n for every integers n .

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The selection of the duty is all real numbers.