# 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

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

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

Related posts:

1. The Trigonometric Functions. The trigonometric functions are sin , cos , tan ,...
2. Integration by trigonometric substitution integration by trigonometric substitution: One of the most powerful techniques...
3. Derivatives of inverse trigonometric functions Inverse trigonometric functions  are the  inverse of trigonometric functions ....
4. Derivatives of Trigonometric functions. As you know, The functions SINE x(sin x) , CO-SECANT...
5. Derivative of simple algebraic or polynomial functions. The derivative and calculations on finding derivative of simple algebraic functions...