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Ratios of trigonometry

There are six types trigonometry ratios are there
  1. Sin∅
  2.  Cos∅
  3. Tan∅
  4. Cot∅
  5. Sec∅
  6. Cosec∅

Sin A=opposite of a angle
            Hypotenuse

Cos A=adjcent side
            Hypotenuse

Tan A=opposite
             Adjacent

Examples::1

If tan A =3/4, then find the other trigonometry ratio of angle A. 

Sol::

Given tan A=3/4
Hence tan A=opposite side
                         Adjacent side
    =3/4

Therefore, opposite side:adjacent side
=3:4

For angle A, opposite side=BC=3k
Adjacent side=AB=4k

Now, we have in triangle ABC
                          (By Pythagoras theorem)

AC²=AB²+BC²
=(3k)²+(4k)²
AC²=√25k²
AC=5k=hypotenuse

Now, we can easily write the other ratios of trigonometry
Sin A=3k/5k=3/5
Cos A=4k/5k=4/5.

Sathish Dhuda

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