Answer to Question #223049 in Trigonometry for Frank

Question

Let a=cos(π/3), b=cos(1radian), c=cos(1degree), we have that

A.c a

Answer 1

The function f(t)=cos(t) is decreasing if 0$\le t \le \pi$ .

We have 0<t₁=1 degree <t₂=1 radian $\approx 57^\circ <\pi/3=60^\circ$ , therefore

c=f(t₁)>b=f(t₂)>a=f(t3). So we have B.a<b<c.