Trigonometry is a branch of Math studying the relationship between angles and lengths of the sides. There are six well known trigonometric functions - sine, cosine, cosecant, secant, tangent and cotangent. Trigonometric functions such as sine, cosine and tangent are used in computations in Trigonometry and students need to be comfortable with these functions. Trigonometry is widely applicable in most 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. The technique of triangulation is a part of trigonometry and it is noticeably applied in the field of astronomy. Moreover, this topic is also used in geography, statistics, oceanography, land surveying, geodesy, civil engineering, architecture and many other areas.

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Trigonometry is all about the relation of triangles. It is a part of Mathematics which gives basic to advanced level concepts. TutorVista provides online learning help for all grades. Its online sessions are personalized, complete and understandable which helps students manage their daily lessons. Students of higher grades can also schedule online sessions with TutorVista and make their learning methods effective and easy at all times. Moreover, college trigonometry help is also offered by TutorVista.

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All essential trigonometry topics are requisitely covered by the TutorVista online learning sessions. Some sub-topics are mentioned below and students are requested to study them to get better understanding about the topic.

**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 it. Certain basic definitions and formulas are to be remembered for the best of understanding and to have a right approach towards the subject. Mathematics is not just about learning formulas it’s a way of thinking and solving many problems to develop your skills. We considered six possible combinations between the ratios of two sides of a triangle to solve various problems which are sine, cosine and tangent. These three functions are simply ratios of the sides of triangles that help us relate to an angle in the triangle.

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 $\theta$ refers to a particular ratio. It is not sin multiplied by q.

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

(iii) In right angled triangles the 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.

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