Trigonometric Functions





Trigonometric Functions:

We have already defined the trigonometric functions such as sine , cosine , tangent of any magnitude already here:

trigonometric functions

Now , we consider trigonometric functions for angles of a right angled triangle , and see how they are a special case of trigonometric functions of angle of any magnitude.

 

Suppose ABC is a right angled triangle with hypotenuse “c” ,  “a” the side opposite to the angle \theta and “b” the side adjacent to the angle \theta , as shown in the figures below:

trigonometric functions

trigonometric functions

And we can also show the above right angled triangle in the form of a triangle inscribed in a circle in standard position as:

trigonometric functions

trigonometric functions

 

Then we can define the six trigonometric functions of \theta as follows:

sine:

\sin \theta = \dfrac{BC}{AB} = \dfrac{a}{c} = \dfrac{perpendicular}{hypotenuse}

cosine:

\cos \theta = \dfrac{AC}{AB} = \dfrac{b}{c} = \dfrac{base}{hypotenuse}

tangent:

\sin \theta = \dfrac{BC}{AC} = \dfrac{a}{b} = \dfrac{perpendicular}{base}

cosecant:

\csc \theta = \dfrac{AB}{BC} = \dfrac{c}{a} = \dfrac{hypotenuse}{perpendicular}

secant:

\sec \theta = \dfrac{AB}{AC} = \dfrac{c}{b} = \dfrac{hypotenuse}{base}

cotangent:

\cot \theta = \dfrac{AC}{BC} = \dfrac{b}{a} = \dfrac{base}{perpendicular}

 

Values of trigonometric functions for standard angles:

The values of trigonometric functions for general or standard angles are given in the image below:

Values of trigonometrical functions of standard angles

Values of trigonometrical functions of standard angles

 

 



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