The trigonometric ratios have the right to likewise be thought about as attributes of a variable which is the meacertain of an angle.

This angle meacertain can either be given in degrees or radians . Here, we will usage radians. Because any type of angle via a meacertain higher than 2 π radians or much less than 0 is indistinguishable to some angle with meacertain 0 ≤ θ 2 π , all the trigonometric features are routine .

The graph of the sine function looks like this:

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Keep in mind that the domain of the feature y = sin ( x ) ) is all real numbers (sine is identified for any kind of angle measure), the array is − 1 ≤ y ≤ 1 .

The graph of the cosine function looks favor this:

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

The graph of the tangent feature looks prefer this:

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The doprimary of the attribute y = tan ( x ) ) is all genuine numbers except the values where cos ( x ) is equal to 0 , that is, the worths π 2 + π n for all integers n . The selection of the tangent feature is all genuine numbers.

The graph of the secant attribute looks choose this:

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The doprimary of the function y = sec ( x ) = 1 cos ( x ) is aacquire all real numbers other than the worths wbelow cos ( x ) is equal to 0 , that is, the worths π 2 + π n for all integers n . The variety of the feature is y ≤ − 1 or y ≥ 1 .

The graph of the cosecant function looks like this:

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The doprimary of the attribute y = csc ( x ) = 1 sin ( x ) is all real numbers other than the worths where sin ( x ) is equal to 0 , that is, the worths π n for all integers n . The selection of the function is y ≤ − 1 or y ≥ 1 .

The graph of the cotangent attribute looks favor this:

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The domajor of the feature y = cot ( x ) = cos ( x ) sin ( x ) is all real numbers other than the worths wright here sin ( x ) is equal to 0 , that is, the worths π n for all integers n .


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The selection of the attribute is all actual numbers.