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Mathematics | Trigonometry 3 | English Medium



Through today's lesson we are going to study a little bit more deeper about trigonometry more than the last two lessons. Lets see an easier way to remember the main nine trigonometric ratios we discussed in the last article.
All of you now know that the tan ratios of an angle is equal to the ratio between, the sin ratio of that angle and the cos ratio of it. Which means if we know the sin and the cos values of those three main angles we can derive tan value using them.



If you can remember sin30, sin45 and sin60 then inverse the values of them to get cos30, cos45 and cos60. Then you can derive tan30, tan45 and tan 60 from them.

Lets do some example sums to get a better understanding about the type of questions you are going to get for the O/L examination.

Find the values of sin30.sin60 + cos30.cos60.


sin30.sin60 + cos30.c0s60 = (1/2)(√3/2) + (√3/2)(1/2)
= √3/2


I'll leave this sums to try them yourselves.

1. sin60.sin30 + cos30.cos60
2. sin30cos60 + cos30sin60
3. (sin30)^2 + (cos30)^2
4. (cos30 – sin30)(cos30+sin30)
5. Prove that (tan30 + tan45)/(1-tan30.tan45) = 2 +√3


When I was doing my O/Ls I always had a nagging question about trigonometry, why do we learn trigonometry? To get a clear answer to that question you should learn trigonometry furthermore but for now I will explain it with a simple example.



Imagine there is a somewhat tall rock and we want to measure its height. Here is a simple way of doing it. Assume that the earth is plane considering to the height of the rock. Take a rope and measure its length. Tie a rope to the point where you want to measure the height (point A). Tie the other end to the ground and keep in mind to keep the rope straight. Then measure the angle of the rope with the ground as shown in the figure below. Now we know the AB length we know the required angle so the height of the rock = AB length X sin(measured angle) 




Written by Uncle 

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1 දෙනෙක් අදහස් කිවුවා:

වකා - WAKA said...

(y)

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