Question

precalc question. How to I work back from a fraction to find its angle?

I have like \[\frac{1+\sqrt{3}}{2\sqrt{2}}\]\[\frac{-1+\sqrt{3}}{2\sqrt{2}}\]How am I supposed to see this and figure out that they are \(\cos(\pi /12)\text{ and } \sin(\pi /12)\) respectively?

Answer 1

using a half angle, perhaps

Answer 2

you know cosine 30 degrees and sine 30 degrees, I would use a half angle identity to find this value

Answer 3

I could be way off base, let's see what electrokid has to say

Answer 4

express the given fraction interms of known t-ratio values
\[{1+\sqrt{3}\over 2\sqrt{2}}={1\over\sqrt{2}}\cdot{1\over2}+{\sqrt{3}\over2}\cdot{1\over\sqrt{2}}\\
\quad=\sin(\pi/4)\cdot\cos(\pi/3)+\sin(\pi/3)\cos(\pi/4)\\
\quad=\sin(\pi/4+\pi/3)
\]

Answer 5

@precal thanq :)

Answer 6

this is the sum and difference formulas