by timus
Accordingly to the conventional definition, “trigonometry is that branch of mathematics which deals with relations existing amongst the sides and angles of a triangle.”

Not your cup of tea, huh? Try out the following steps:
1.Take index cards and cut them into small pieces. Small enough to keep in your pocket and large enough to write one single trigonometric identity clearly.

2. Start with writing 1 identity at the back of 1 index card. An example would be Sin Square Theta+Cos Square Theta=1. Now, divide all the terms by Sin Square Theta. Do it your self and see the result. Neatly copy your working on the back of an index card. Write down today’s date. This process will take up 15 minutes at the most.

3. Next time, divide all the terms by Cos Square Theta. Neatly jot down the working at the back of another index card and put down the date.

4. Do similar divisions of other identities.

5. 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.
Let us try solving out a simple problem based on practical application of trigonometry:

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’d rather do something else!

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:info@learningexpress.biz or mailto:learningexpress@getresponse.com or go to: http://www.learningexpress.biz for online help

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