Proof the trig sum and difference identities

[nando94]

My homework is to find the sin or cos value of angle that is not directly known on the unit circle. So of course we are given an equation which adds or subracts known values to get the desired one.

The problem is that I don't think memorizing them is helping me learn. I want to know how the sin(75) = sin(35+45) without readily memorizing them. So far what I did was draw a 30 degree triangle on the unit circle and then adjacent to the hypotenouse, I drew the 45 degree triangle. Then I drew a 75 degree triangle and tried to reason it through from the there but its not working. So can someone clarify why these identities work.

 

[Mentallic]

Have you studied complex numbers, and specifically DeMoivre's theorem? Because if you haven't, memorizing the formula is going to be a lot easier than proving it each time in your exam.

http://www.themathpage.com/atrig/sum-proof.htm

 

[nando94]

Nah my class is not that far yet. Everything is nearly culminating to calc now.

 

[Mentallic]

Then if you want to understand why the identities work, you'll have to work your way through the proof that I linked. If there are any parts you don't understand in the proof, you can always ask us to help clarify it for you

Or you can take the easy road out and just accept it, because in the end you'll still have to memorize the formula.

 

[nando94]

Thanks. I will check it out and see if it answers my question. I would rather take the hard road and understand what I am doing so that I can apply it better. Also are these identities used a lot in calc? I am going to take it next year.

 

[Mentallic]

I would rather take the hard road and understand what I am doing so that I can apply it better.

Sure, I understand that.

Also are these identities used a lot in calc? I am going to take it next year.

Not so much in calc, but the trig sums continue to appear in many different applications throughout your schooling - even in college/university. So it's definitely worth memorizing. Try to get a feel for the patterns that sin(A+B) has as then cos(A+B). Tan always seemed to be the easiest to remember, maybe because it wasn't similar to any other trig.