How do you evaluate arc cos(-1/2)arccos(12)?

1 Answer
Nov 26, 2016

arccos(-1/2)=(2pi)/3arccos(12)=2π3

Explanation:

arccosxarccosx is an angle whose cosine ratio is -1/212.

Now as cos(pi/3)=1/2cos(π3)=12 and cos (pi-A)=-cosAcos(πA)=cosA

cos(pi-pi/3)cos(ππ3) i.e. cos((2pi)/3)=-coe(pi/3)=-1/2cos(2π3)=coe(π3)=12

As cos((2pi)/3)=-1/2cos(2π3)=12, we have

arccos(-1/2)=(2pi)/3arccos(12)=2π3