Question

Question #139ce

Answer 1

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:

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.