Question #139ce

1 Answer
Parabola
Jan 6, 2018

The answer is:#a=1.10714871+pin#

Explanation:

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

Now, let's do something to strengthen your understanding:
Remember that #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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