Question #139ce

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Question #139ce

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Answer 1 · 2018-01-06T03:00:21

The answer is: $a = 1.10714871 + π n$ $a=1.10714871+pin$

Explanation:

If you plug this into the calculator as $arctan (2)$ $arctan(2)$ , you get the answer:
$a = 1.10714871 + π n$ $a=1.10714871+pin$
There are infinitely many values that make sense, since we can keep rotating the angle around $π$ $pi$ radians around the unit circle.

Now, let's do something to strengthen your understanding:
Remember that $tan θ = \frac{sin θ}{cos θ}$ $tantheta=sintheta/costheta$ which really represents: $(Deltay)/(Deltax)$ .
This question is asking us this:
"At what angle does the slope equal 2?"

If $tana=2$ ,
$tana=(2sina)/cosa$
Therefore, we are trying to solve $a$ in the picture:
I made this
Now, using the Pythogorean theorem, we can find $x$ .
$1^2=x^2+(2x)^2$
$1=x^2+4x^2$
$1=5x^2$
$1/5=x^2$
$sqrt (1/5)=x$

Therefore, the two legs are $sqrt (1/5)$ and $2sqrt(1/5)$ which means that $sqrt(1/5)=cosa$ and $2sqrt(1/5)=sina$

It is interesting of how you can figure out so much with just an information.

You can use these information to double check whether you were right or not.

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Question #139ce

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