How to evaluate $\cos(22^\circ)\cos(38^\circ) - \sin(22^\circ)\sin(38^\circ)$?

Question

How does one evaluate this? Does this generalize to $\cos(x)\cos(y) - \sin(x)\sin(y)$?

@Dr.SonnhardGraubner What's wrong with radian angles, if those were given instead? — Cookie, Jan 07 '15 at 20:55

score 1 · Answer 1 · answered Jan 07 '15 at 20:51

1

$$\cos(22)\cos(38)-\sin(22)\sin(38)=\cos(22+38)=\cos(60)=\frac{1}{2}.$$

answered Jan 07 '15 at 20:51

idm

score 1 · Answer 2 · answered Jan 07 '15 at 21:48

1

A standard identity says $\cos x\cos y-\sin x\sin y=\cos(x+y)$, so you have $\cos(22^\circ+38^\circ)$.

answered Jan 07 '15 at 21:48

Michael Hardy

2 Answers2