How do you use a half-angle formula to find the exact value of #cos((3pi)/8)#?
1 Answer
Mar 18, 2018
Explanation:
#"using the "color(blue)"half angle formula"#
#•color(white)(x)cos(x/2)=+-sqrt((1+cosx)/2)#
#(x/2)=(3pi)/8rArrx=(3pi)/4#
#rArrcos((3pi)/8)=+-sqrt((1+cos((3pi)/4))/2)#
#(3pi)/8" is in first quadrant "#
#=+sqrt((1-cos(pi/4))/2)#
#=+sqrt((1-1/sqrt2)/2)=+sqrt((1-sqrt2/2)/2)=sqrt((2-sqrt2)/4)#
#rArrcos((3pi)/8)=1/2sqrt(2-sqrt2)#
