Why does the trigonometry of obtuse angles use ref angles?

[shirozack]

TL;DR Summary

Why does the trigo of obtuse angles use ref angles?

I would like to know the "why" of trigo of non acute angles in a unit triangle. why is it equals to the reference angle? how did it even come about?

For example, sin 150 degrees. why is it equal to sin 30?

i understand sin 30 because there is a right angle triangle of opposite and hypoteneuse etc.

but how did we resolve sin 150? how did answer became calculating the reference angle to the x-axis? why not calculate it based on the y-axis? if sin is defined as the ratio of the opposite to the hypo, then where is the opposite and hypo of a 150 angle? why is sin150 = sin30?

thanks

 

[mcastillo356]

Hi, @shirozack

TL;DR Summary: Why does the trigo of obtuse angles use ref angles?

https://en.wikipedia.org/wiki/Unit_circle

I would like to know the "why" of trigo of non acute angles in a unit triangle. why is it equals to the reference angle? how did it even come about?

For example, sin 150 degrees. why is it equal to sin 30?

I prefer radians: https://en.wikipedia.org/wiki/Radian

i understand sin 30 because there is a right angle triangle of opposite and hypoteneuse etc.

but how did we resolve sin 150? how did answer became calculating the reference angle to the x-axis? why not calculate it based on the y-axis? if sin is defined as the ratio of the opposite to the hypo, then where is the opposite and hypo of a 150 angle? why is sin150 = sin30?

thanks

Hope it helps. At any nearby library you will for sure find basic trigonometry bibliography. I recommend you not to get messed with the links. Just stare at them for a while, and no more.

Best wishes!