Question

一道数学题，题目如图所示。要求写出详细解答过程！我先谢谢大神们了！在线等！

Answer 1

（1）sinx在[π/2，π]递减
所以sin2π/3﹥sin4π/5
（2）sin(-110°)=-sin(70°)
sin(-820°)=sin(-100°)=-sin(80°)
∵sin(70°)＜sin(80°)
∴-sin(70°)＞-sin(80°)
∴sin(-110°)＞sin(-820°)
（3）sin(314°）=sin(360°-46°)=-sin(46°)<0
sin(769°）=sin(720°+49°）=sin(49°)>0
所以 （314°）〈sin(769°)

Answer 2

（1）sin2π/3=sin120°
sin4π/5=sin144

由于sinx在[90°，180°]上单调递减，所以sin120°>sin144°，也就是sin2π/3>sin4π/5
（2）sin(-820°)=sin(-820°+360°×2)=sin(-100°)
由于sinx在[-180°，-90°]上单调递减，所以sin(-110°)>sin(-100°)，也就是sin(-110°)>sin(-820°)
（3）sin(-314°)=sin(-314°+360°)=sin(46°)
sin(-769°)=sin(769°-360°×2)=sin(49°)
由于sinx在[0°，90°]上单调递减，所以sin49°>sin46°，也就是sin(-314°)< sin(-769°)
（4）sin(-54π/7)=sin(-54π/7+28×2π/7)=sin(2π/7)
sin(-63π/8)=sin(-63π/8+32×2π/8)=sin(π/8)
由于2π/7∈[0,π/2]，π/8∈[0,π/2]，2π/7>π/8且sinx在[0,π/2]单调递增，所以sin(2π/7)>sin(π/8)，那么也就是sin(-54π/7)>sin(-63π/8)
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