Question

30 PTS!!! ANYONE GOOD AT MATH PLS HELP!

Find the exact value of sin(arctan(2)). Explain full reasoning in detail, please.

Answer 1

`(2)/(√(5) )`

Explanation:

To solve this, all we need to do is draw a triangle.

From the
`arctan(2)` we can deduce that
`tan(x)=(2)/(1)`

From that, we can draw our triangle as we know that tan(x) is the opposite side over the adjacent side. Attached is that triangle. Through the Pythagorean Theorem, we can find that the hypotenuse of this right triangle is
`√(5)`

Now all we need to do is take the sin of this triangle, which is the opposite side over the hypotenuse

This gives us the value of
`(2)/(√(5) )` which is our answer.