Question

find value of angle a (sin2a-10)=(cos+40)​

Answer 1

Answer:

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Step-by-step explanation:

you only concentrate on the sin/cos graph between 0 and 90 degrees, the graph almost looks like a straight line. One can exploit this property to predict a very close approximate for any sin/cos value between 0 and 90 degrees.

The thing about straight line graphs is that the y values increase at a uniform rate with increase in x values. So suppose I need to find sin(15).

Sin(15)= [Sin(0)+Sin(30)]/ 2

We get sin(15) approcimately as 0.25, which is a very good approximate. Sin(22.5) can be approximated as an average of Sin(15) and Sin(30), and so on.

You will obviously need to memorize some few standard values to begin with, namely sin(x)={x=0,30,45,60,90).

Same goes for cos(x). Exactly the same method. And since the rest of the trigonometric angles can be rewritten in form of Sin and Cos you can evaluate them too. For angles greater than 90 use the transformation formulates first.

Obviously this method becomes a little tedious when you have to keep finding averages to close in on a particular peculiar angle( for ex- 27 degrees: average of 0 and 30 gives 15, then average of 15 and 30 gives 22.5, then average of 22.5 and 30 gives a close enough approximation for 27).

I have been using this method for quite a while now to find values when I'm in a hurry and want a quick approximate without a calculator. Similar approach can be extended to find logarithms for any value without a calculator too ;).