Trigonometric Functions

Topics are arranged as per SYLLABI published by Maharashtra State Board of Secondary and Higher Secondary Education.

Trigonometric Functions

Trigonometry is measurement triangles.
Measurement of sides, angles and various relations exists between them.
In broad categories there are two types of Trigonometric Functions:

Circular : They are used to study periodic phenomena (Ex: sin x )
Hyperbolic : They are analogous to Circular Functions (Ex: sinh x )

For the scope of our study, we’ll focus only on Circular Functions.
Three mains trigonometric functions can be studied with the help of "Right angled Triangle"

There are three are three main trigonometric functions.

Sine (sin) = Opposite / Hypotenuse
Cosine (cos) = Adjacent / Hypotenuse
Tangent (tan) = Opposite / Adjacent = Sine / Cosine

Three important functions are best defined using the above three main functions.

Secant (sec) = 1 / Cosine = Hypotenuse / Adjacent
Cosecant (cosec) = 1/ Sine = Hypotenuse / Opposite
Cotangent (cot) = 1 / Tangent = Adjacent / Opposite

Fundamental identities: [Note: Sine, Cosine and Tangent are all based on a Right-Angled Triangle.]

where

Trigonometric Equations and Their Solution

The equation that involves a trigonometric ratio of variables is called a Trigonometric Equation.
The values of variables present in trigonometric equation for which the equation is satisfied is called the solution of that trigonometric equation.
There can be infinitely many values that satisfy trigonometric equation, but out of these values those which lie in the interval are called the principal solutions.
If solutions of a trigonometric equation are generalized by using its periodicity and represented by an equation or a formulae, they are called the general solutions of the trigonometric equations.

General Solutions of Trigonometric Equations

Trigonometric Equation	General Solution	Key Points


		General solution is same as that of
=	;
=	;
=	;
=	;
=	;
=	;

Polar coordinates: Polar and Cartesian co-ordinates of a point are related.
Where and for
In polar coordinate system; we’ve fixed point called as pole. It’s equivalent to origin in Cartesian co-ordinate system.

Triangle can be expressed in three parts.
The three sides and three angles of a triangle are together known as parts of the triangle.
If at least three of them are known (atleast one is its side), then the rest three can be obtained. The process of obtaining unknown parts of a triangle is called as solving the triangle or solution of triangle.

Let’s assume there is a triangle ABC having side BC = a, CA=b and AB=c . Let’s go through various rules and theorems for solving triangles.