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.
Ishani Dutta is an educator who specializes in providing online tuition packages for Mathematics and English. For similar tips on different topics like pre-algebra, co-ordinate geometry, essay writing mailto:
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