令u=x-4/π, 2x=2u+8/π;
sinu=√2/10; cosu=7√2/10;
sin2x=sin(2u+8/π)=2con8/π.sinu.cosu+sin8/π.(2cosu^2-1)=7.(cos8/π)/25-24.(sin8/π)/25;
sin(2x+3/π)=sin(2u+11/π)=7.(cos11/π)/25-24.(sin11/π)/25;
因为8/π和11/π是定值,所以不用再化简了.
要求近似值时,sin8/π=0.561; cos8/π=-0.828; sin11/π=-0.352; cos11/π=-0.936;代入得
sin2x=0.770;
sin(2x+3/π)=0.077;