# Demonstrate that sin 4 radians < sin 3 radians.

*print*Print*list*Cite

### 1 Answer

`pi rad=3.14 rad`

`4 rad=(3.14+.86)rad`

`=(pi+.86)rad`

`3rad=(3.14-.14)rad`

`=(pi-.14)rad`

Thus

`sin(4rad)=sin((pi+.86)rad)=-sin(.86rad)` (i)

`sin(3rad)=sin((pi-.14)rad)=sin(.14rad)` (ii)

from (i) and (ii)

sin(4rad) < sin(3rad)

because sin(4 rad)<0 and sin(3 rad)>0.