Question

已知sin(π÷6－α）＝1÷4,则sin（π÷6＋2α）＝

Answer 1

设A为ALPHA;前式sin(3.1416/6)cosA-cos(3.1416/6)sinA=0.25;cosA/2-1.732*sinA/2=0.25;解之;得A=0.270926,即15.52288度;
后式=sin(3.1416/6)cos2A+cos(3.1416/6)sin2A=0.874994
a sin(p)+bsin(p)=d;平方;a^2s^2+b^2c^2+2absc=d^2;a^2s^2+b^2c^2-d^2=-2absc;再
平方(a^2s^2+b^2c^2)^2-2d^2(a^2s^2+b^2c^2)+d^4=4a^2b^2s^2c^2;a^4s^4+b^4c^4+2a^2b^2s^2c^2-
2d^2(a^2s^2+b^2c^2)+d^4=4a^2b^2s^2c^2;利用c^2=1-s^2;化去c^2,c^4,设t=s^2;解二次式得s^2;根号下;如是求得sin(p)值

Answer 2

sin(pi/6+a)=1/4
--->cos[2(pi/6+a)=1-2[sin(pi/6+a)]^2=1-2(1/4)^2=7/8
--->cos(pi/3+2a)=7/8
又cos(pi/3+2a)=sin[pi/2-(pi/3+a)]=sin(pi/6-2a)
--->sin(pi/6-2a)=7/8.