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 Sin² theta+Cos² theta=1. Now, divide all the terms by Sin² theta. Do it your self and see the result. Neatly copy your working on a pocket size notebook. Write down today’s date. This process will take up 15 minutes at the most.
2.Next time, divide all the terms by Cos ² theta. Neatly jot down the working in your notebook and put down the date.
3.Do similar divisions of other identities.
4.If you do this once a day for just 3 weeks, you will understand which formula to use when a trigonometry problem stares at your face the next time around. If you still have problems, you can always ask your teacher in school or you can refer the problem to an online tutor. A reasonable good online math tutor should be able to help.
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.
Step1:to start with, first draw the required diagram according to the problem.
P
M O
Step2: Try relating the diagram with the given problem
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.
Solve this problem and forget about solving 15 problems. You can move onto tougher problems.
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