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Trigonometric Functions

The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle.

This angle measure can either be given in degrees or radians . Here, we will use radians. Since any angle with a measure greater than 2 π radians or less than 0 is equivalent to some angle with measure 0 θ < 2 π , all the trigonometric functions are periodic .

The graph of the sine function looks like this:

Math diagram

Note that the domain of the function y = sin ( x ) ) is all real numbers (sine is defined for any angle measure), the range is 1 y 1 .


The graph of the cosine function looks like this:

Math diagram

The domain of the function y = cos ( x ) is all real numbers (cosine is defined for any angle measure), the range is 1 y 1 .


The graph of the tangent function looks like this:

Math diagram

The domain of the function y = tan ( x ) ) is all real numbers except the values where cos ( x ) is equal to 0 , that is, the values π 2 + π n for all integers n . The range of the tangent function is all real numbers.


The graph of the secant function looks like this:

Math diagram

The domain of the function y = sec ( x ) = 1 cos ( x ) is again all real numbers except the values where cos ( x ) is equal to 0 , that is, the values π 2 + π n for all integers n . The range of the function is y 1 or y 1 .


The graph of the cosecant function looks like this:

Math diagram

The domain of 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 values π n for all integers n . The range of the function is y 1 or y 1 .


The graph of the cotangent function looks like this:

Math diagram

The domain of the function y = cot ( x ) = cos ( x ) sin ( x ) is all real numbers except the values where sin ( x ) is equal to 0 , that is, the values π n for all integers n . The range of the function is all real numbers.






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