Addition formulae - Trig help requested

[kalistella]

addition formulae - Trig help requested!

I have a problem with this with regard to Sin 120 or Cos 120.

Eg

sin 165
sin (120 +45)
sin120.cos45-cos120.sin45

How do I deal with sin 120 or cos 120?

I know that cos 45 is 1/square root 2 and so is sin 45.

But in the above problem, the answer comes to 1/4 (square root 6 - square root 2)

I don't get this answer. My problem is with the 120 angles.
Please help!

Thanks!

 

[arildno]

Well, learn the correct addition formula properly.
Then, look at the unit circle what sin(120) and cos(120) should be.

 

[marlon]

sin (120 +45)
sin120.cos45-cos120.sin45

This is wrong. Check your addition formula again.

marlon

 

[HallsofIvy]

As arildno and marlon have already pointed out, you have the sine sum formula wrong! As for 120 degrees what fundamental angles do you know sine and cosine for? (You seem to have 45 degrees okay.) Would it help to remember that 120= 60+ 60 or that 120= 90+ 30?