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Little known Tricks of Trigonometry

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Not your cup of tea, huh? Try out the following steps:
1. Start with writing 1 identity on a piece of paper. An example would be Tan2+1=Cosec2. Divide the paper vertically into 3 columns.
2. In the first column, divide all the terms by Sin2 and write down the results.
3. In the next column divide all the terms by Cos2 and write down each step.
4. Next divide all the terms by Tan2 and write your results in the third column.
5. What do you see?
I will tell you the first 3 things that I observed when I did it myself as a kid.
1. You can move from any column to the other just by multiplying or dividing all the terms by Sin2 or Cos2 or Tan2.
2. There is only one fundamental formula that I need to remember. Everything else in the entire is derived through multiplications and divisions.
3. I can also get values of say, Cos60 if I know the value of Sin60. How do I get that? Sin60 =√ 3/ 2. Thus Sin260=3/4.
We know that Sin2+Cos2=1. Therefore, Cos2=1- Sin2=1-3/4=1/4.
So, Cos=1/2.Simple!

Now, Let us try solving a simple problem:
A kite is flying at a height of 75 meters from the level ground, attached to a string inclined to an angle of 60 degree to the horizontal. Find the length of the string to the nearest meter.

Declare the necessary assumptions:

Let 'P? denote the position of the kite, and MP = 75 meters (the height of the kite)

And the string be held at the point O, The angle < MOP = 60 degree (given)

Therefore, OP is the length of the string


Step3: The next step is to apply the appropriate identities.

From the right angled triangle MOP,

OP = opposite leg of the acute angle < MOP

MP = hypotenuse

We will apply a basic trigonometric identity here

i.e., (opposite leg) / (hypotenuse ) = Sin < MOP

[As < MOP is the acute angle and the ratio Sine < MOP is the ratio between opposite leg to the hypotenuse.]

We have,

(OP) / (M P) = Sin < MOP

(OP) / (MP) = Sin 60 [< MOP = 60 (given)]

OP = (Sin 60) * (MP)

OP = (sin 60) * 75 [MP = 75 (given)]

OP = ((√ 3) / 2) * 75 [Sin 60 = ((√ 3) / 2) [value of Sin60 can easily be found out using trigonometric tables of standard angles]

O P = ((1.732) / 2) * 75 [(√ 3) = 1.732 (approx.)]

OP = 86 .6 [approx. ]

So, the length of the string is 86.6 meters (to the nearest meter)


For grasping a chapter thoroughly you must solve at least fifteen problems.
If you don?t want to work that much, try solving the following problem:

A pole is being broken by the wind; the top struck the ground at an angle of 30 degree and at a distance of 8 m from the foot of the pole. Find the whole height of the pole.



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