Trigonometry is an imperative topic of mathematics. It is widely applicable in almost of the fields related to science and technology. Trigonometry is all about the study of relationships related to angles of triangles and lengths of sides. There are six well known trigonometric functions - sine, cosine, cosecant, secant, tangent and cotangent.

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**Right angle Triangle****Pythagoras theorem****Trigonometric identities****Sine and Cosine Law****Trigonometric Tables****Heights And Distance****Trigonometric Ratios**

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With trigonometry we can find the height of a building or the width of a river without actually climbing or crossing. Certain basic definitions are necessary to further develop this subject. We considered six possible combinations between the ratios of two sides of a triangle to solve various problems.

In this subject we usually use the Greek letters.

(i) $\alpha$ (Alpha) (ii) $\beta$ (Beta) (iii) $\theta$ (Theta)

(iv) $\gamma$ (Gamma) (v) $\phi$ (Phi) (vi) $\lambda$ (Lambda)

and so on to indicate the measure of an angle.

Let us call $\angle$ A as $\theta$.

The side opposite to $\theta$ is BC.

The side adjacent to $\theta$ is AB.

The hypotenuse of the $\triangle$ABC is AC.

Now, let us write down the trigonometrical ratios with the help of the above triangles:

(i) $Sine \ \theta$ : It is defined as the ratio of the side opposite to $\theta$ and the hypotenuse.

i.e. $Sine \ \theta$ = $\frac{Opposite \ side}{Hypotenuse}$ = $\frac{BC}{AC}$

In short we write $sin \ \theta$ = $\frac{BC}{AC}$

(ii) $Cosine \ \theta$ : It is defined as the ratio of an adjacent side to $\theta$ and the hypotenuse.

i.e. $Cosine \ \theta$ = $\frac{Adjacent \ side}{Hypotenuse}$ = $\frac{AB}{AC}$

In short, $cos \ \theta$ = $\frac{AB}{AC}$

(iii) $Tangent \ \theta$: It is defined as the ratio of the side opposite to $\theta$ and the adjacent side.

$Tangent \ \theta$ = $\frac{Opposite \ side}{Adjacent \ side}$ = $\frac{BC}{AB}$

In short, $tan \ \theta$ = $\frac{BC}{AB}$

Similarly three more ratios can be obtained by taking the reciprocals of $sin \ \theta$, $cos \ \theta$ and $tan \ \theta$.

(iv) $Cosec \ \theta$ is the reciprocal of $sin \ \theta$.

It is written as $Cosec \ \theta$,

$\therefore$ $cosec \ \theta$ = $\frac{1}{sin \ \theta}$

(v) $Sec \ \theta$ is the reciprocal of $cos \ \theta$.

It is written as $sec \ \theta$,

$\therefore$ $sec \ \theta$ = $\frac{1}{cos \ \theta}$

(vi) $Cot \ \theta$ is the reciprocal of $tan \ \theta$.

It is written as $cot \ \theta$,

$\therefore$ $cot \ \theta$ = $\frac{1}{tan \ \theta}$

(i) Sin $\theta$ means a particular ratio. It is not sin multiplied by q.

(ii) For trigonometrical ratios, short form T-ratios will be used.

(iii) In right angled triangles T-ratios are obtained only for acute angles.

(iv) T-ratios depend on only the magnitude of the angles and not on the size of the triangle.