## 12.20.2014

### Arctangent of the calculator

Sorry to trouble you.
My wife is studying trigonometry, she learns in the legal (!) Institute (small computer science course - to "work with the calculator"). I studied Algebra 10 years ago, but with sines and cosines,  I somehow figured out.
In the impasse puts me "elementary" question ...
We have tg3x = 4, it is necessary to calculate the angle "x" ...
I do not know how to approach this issue ...
Explain it to me please ... Thank you.

Tame this beast through the inverse trigonometric functions. In this case it is necessary to use the arctangent. It looks approximately like this:

tg3х=4
arctg(tg3х)=arctg4

Then quite simply, I explain to the legal institute. Arctangent of tangent is just a corner, in this case 3x. It's like that steal and put back. The literal translation of mathematical language to household will sound like this:

"The Tangent stole of the angle 3x" - tg3x;
"Tangent stole and put in place a corner 3x" - arctg (tg3x)

Now it is a children's question: "What lies at the place?". That's right, the angle 3x. On the left side we have understood.

Now right-hand side. The police discovered that the fence number 4. Police know that traded stolen fence corner on the number at the rate of a tangent. The question arises: "What angle was stolen, if a fence to get him the number 4?". In this case, we can use a table of values of the trigonometric tangent function as a price list on the exchange of angles among the fence.

But we have set the theme of "work with a calculator." The calculator "Windows" enter the number 4, then click the button "Inv". At the same time closely following button "tan". This button should appear degree minus one. Four should remain unchanged. Now press the button tangent to the minus first degree and obtain the value of the angle whose tangent is 4. If we have included in the calculator button "Degrees", then we get 75.963756532073521417107679840837 degrees when the button is turned "Radian", we'll get 1, 3258176636680324650592392104285 radians.

Now we can restore the picture to commit a crime (in degrees and radians oil paintings look different). We write from the beginning in degrees, rounded to three characters:

tg3х=4
arctg(tg3х)=arctg4
3х=75,964
х=75,964/3
х=25,321 (degrees)

The same, but now in radians:

tg3х=4
arctg(tg3х)=arctg4
3х=1,326
х=1,326/3

If you're holding a calculator any other design, you will need an educated bet calculator dig out the desired result.

Unexpected response:

A huge thank you for a mathematical investigation. Your explanation is very inspired us and my wife and I decided all the "problems with a calculator." Thanks again!
P.S. I read your profile in Google. As a citizen of Russia say that I share your views on terrorist organizations of Donetsk and Lugansk. I wish you and the Ukrainian people defeat the terrorists and to regain the Crimea. We believe in Ukraine without the Kremlin! Good luck to you!