Introduction:Are you ready …..Let’s start with triangles, start with TRIGONOMETRY.In simple word, it is a branch of Mathematics which helps in measuring the triangles. There is fixed relationship between angle and their sides in right angle triangle, one angle is exact of 90° and sum of all the interior angles is equal 180°. Why Trigonometry?? Is there any use?? What we can get from it??There are so many questions… Trigonometry is used in various areas. It can be used in measuring the heights or widths or length of the building, can be used in finding the distances between two, can be used in navigation, can be used in oceanography etc….
. Let’s start:Types of Angles:Between 0° to 90° – Acute angle Equals to 90° – Right angle Between 90° to 180° – Obtuse angle Equal to 180° – Straight angleIn a right angle triangle, Longest side, which is opposite to right angle is called “Hypotenuse”. Side which is opposite to Angle A is called “Opposite”. Side which is adjacent to Angle A is called “Adjacent”.
No need to remember, only check Angle A. Change in position of Angle will change the name of the side. But Hypotenuse side will remain same.Ratios and its abbreviations:In right angle triangle there are SIX ratiosSine ? Sin ?Cosine ? Cos ?Tangent ? Tan ?Cosecant ? Cosec ?Secant ? Sec ?Cotangent ? Cot ?Most commonly used are first three ratios.
Formula: OppositeSin ? = ————– HypotenuseAdjacentCos ? = ————– HypotenuseIn short, remember only first two formulas, rest you will find yourself. And for that also, you remember only first, and for remembering “Always keep your Sense of Humour alive”. By this you can remember the first formula, formula of Sin. Sense word stands for Sin, Of stands for Opposite and Humour stands for Hypotenuse. Now, for Cos, which side remains? Yes, only Adjacent.Now coming to Third formula – TanFormula 1 Sin ? Opposite / Hypotenuse OppositeTan ? = ————— = ———– = —————————— = ————– Formula 2 Cos ? Adjacent / Hypotenuse AdjacentNow forth – Cosec and fifth – Sec formulaFor remembering, let’s remember – Mirror image of SC is CSSC means Sin-Cosec and CS means Cos-Sec 1 HypotenuseCosec ? = ———– = ——————– Sin ? Opposite 1 HypotenuseSec ? = ———– = ——————– Cos ? AdjacentLast formula – Cot. Take the help of third formula i.
e. Tan 1 AdjacentCot ? = ———– = ——————– Tan ? OppositeQuestion: Find the values of all the Ratios taking length as given above in the diagram.