
Arthur D. answered 01/13/18
Effective Mathematics Tutor
cos(∏/24)=cos(7.5º)
first find cos(15º)
cos(15º)=cos(45º-30º)
use the identity cos(x-y)=cosxcosy+sinxsiny
cos45cos30+sin45sin30=
(√2/2)(√3/2)+(√2/2)(1/2)=
√6/4+√2/4=
(√6+√2)/4
cos(15º)=(√6+√2)/4
now use the half-angle formula cos(15º/2) because we know cos15º
cos(x/2)=√([1+cosx]/2)
√([1+cos15]/2)=
√([1+(√6+√2)/4]/2)=
√([4+√6+√2]/4)/2=
√([4+√6+√2]/8)=
√(4+√6+√2)/√8=
√(4+√6+√2)/√8=
√[(4+√6+√2)/2√2] is the exact value of cos(7.5º)
Also, I suppose you can rationalize the denominator if you like.
Sheila R.
When I use the calculator to get cos(pi/24), I get .9999973902, but when I type in the above answer, I get .9914448614. Should there be that much of a difference?02/12/19