I have a question on a test, but have no clue how to work the problem. My instructions are to evaluate the expression exactly:
sin (arctan 2)
My possible answers are:
A=5sq rt 2/2
b=2 sq rt5/5
c=2sq rt 5
d 5 sq rt 2
Draw a right triangle; the particular dimensions don't matter.
Label the non-right base angle as $\displaystyle \theta$.
By definition, $\displaystyle \arctan(2)\, =\, \theta$ means that $\displaystyle \tan(\theta)\, =\, 2\, =\, \frac{2}{1}$
So label the "opposite" and "adjacent" sides of the triangle to reflect this.
Use the Pythagorean Theorem to find the value of the hypotenuse.
Since $\displaystyle \arctan(2)\, =\, \theta$, then $\displaystyle \sin(\arctan(2))$ means $\displaystyle \sin(\theta)$.
Read the value of the sine from your picture.