作业帮已知cos(x+π/12)=-5/13,x是第三象限角,求cos(x-π/6)的值
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已知cos(x+π/12)=-5/13,x是第三象限角,求cos(x-π/6)的值
已知cos(x+π/12)=-5/13,x是第三象限角,求cos(x-π/6)的值
已知cos(x+π/12)=-5/13,x是第三象限角,求cos(x-π/6)的值
x第三象限,cos(x+π/12) <0 = >x+π/12 也在第三象限 ＝>sin(x+π/12)<0
=>sin(x+π/12) = -12/13
cos(x-π/6) = cos(x+π/12 - π/4)=cos(x+π/12)cos( π/4) + sin(x+π/12)sin( π/4) =-5/13 * √2/2 - 12 /13 *√2/2 =-17 √2/26
1123
456.23
x第三象限
cos(x+π/12)<0
所以x+π/12第三象限
则cos是增函数
-5/13>-1/2
所以x+π/12>2kπ+4π/3
所以x-π/6也是第三象限
x-π/6的sin和cos都小于0
cos(x+π/12)=-5/13
sin(x+π/12)=-12/13
cosπ/4=√2/2
cos[...
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x第三象限
cos(x+π/12)<0
所以x+π/12第三象限
则cos是增函数
-5/13>-1/2
所以x+π/12>2kπ+4π/3
所以x-π/6也是第三象限
x-π/6的sin和cos都小于0
cos(x+π/12)=-5/13
sin(x+π/12)=-12/13
cosπ/4=√2/2
cos[(x+π/12)-(x-π/6)]=√2/2
令a=x-π/6
所以-5/13*cosa+(-12/13)sina=√2/2
(-12/13)sina=√2/2+5/13*cosa
平方
144/169(1-cos²a)=1/2+5√2/13cosa+25/169cos²a
cos²a+(5√2/13)cosa-119/338=0
cosa<0
取负数解
cosa=[-5√2/13-12√2/13]/2
所以cos(x-π/6)=-17√2/26
收起
x是第三象限角所以sin（x+π/12）<0所以sin（x+π/12）=-12/13
cos(x-π/6)
=cos(x+π/12-π/4)
=cos(x+π/12)cos(π/12)+sin(x+π/12)sin(π/4)
=-17(2)½/26