Making trigonometry easy to learn

Trigonometry is one of the branches of mathematics that is associated with angles of triangles. Trigonometric functions are used to relate the angles of a triangle to its lengths of the sides. We are introduced to the various trigonometric functions in our high school. Sine, cosine and tangent are the most familiar trigonometric functions that we come across.

Understanding the various trigonometric functions can be a little confusing for everyone. Sine, cosine and tangent are all associated with right angled triangles. A right angled triangle is one in which one side of the triangle is 900. Cos, sin and tan can be calculated with the various sides of a right angled triangle. A small pictorial depiction is given below.

The above representation can be simply read as:

Sine = opposite ÷ hypotenuse

Cosine = adjacent ÷ hypotenuse

Tangent = opposite ÷ adjacent

Let me explain these with the help of an example. Consider the following:

Angle – 350 Opposite = 3.5cms
Hypotenuse = 7 cms Adjacent = 6cms

Finding out the Sin, Cos and Tan using the above information goes like this:

The formula to calculate Sine = opposite ÷ hypotenuse. Therefore, using the same you will get 3.5/7=0.5

The formula to calculate Cosine = adjacent ÷ hypotenuse.  Therefore, using the same you will get 6/7=0.857

The formula to calculate Tangent = opposite ÷ adjacent. Therefore, using the same you will get 3.5/6= 0.584.

Keep the image in mind and everything will fall in place very easily. This was a very simple explanation of the trigonometric functions – sine, cosine and tangent. It would just be interesting to note that the trigonometric functions that we use today have been developed in the medieval period, making them very very old. They can be considered as some of the most antique functions that we use.

Sine and cosine can be traced back to the Gupta dynasty. Each of the words have their own derivations. Sine was derived from a Sanskrit word which was transliterated in Arabic and mistranslated into Latin leading to ‘Sinus’, which was later converted to the Latin word ‘Sine’. The other word tangent is derived from the Latin word ‘Tangere’ meaning ‘to touch’. Cosine was written as ‘co.sine’, meaning ‘complimentary sine’ which got shortened to the present ‘cosine’.

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