作业帮三道关于高一三角函数的题目1)求值cos(π/5)cos(2π/5)2)求函数y=1-(cosx)^2+(cosx)^4的最小正周期3)求函数y=2sinx(sinx+cosx)的减区间1)0.25 2)π/4 3)[kπ+3/8π,kπ+7/8π]
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![三道关于高一三角函数的题目1)求值cos(π/5)cos(2π/5)2)求函数y=1-(cosx)^2+(cosx)^4的最小正周期3)求函数y=2sinx(sinx+cosx)的减区间1)0.25 2)π/4 3)[kπ+3/8π,kπ+7/8π]](/uploads/image/z/15044226-42-6.jpg?t=%E4%B8%89%E9%81%93%E5%85%B3%E4%BA%8E%E9%AB%98%E4%B8%80%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E9%A2%98%E7%9B%AE1%29%E6%B1%82%E5%80%BCcos%28%CF%80%2F5%29cos%282%CF%80%2F5%292%29%E6%B1%82%E5%87%BD%E6%95%B0y%3D1-%28cosx%29%5E2%2B%28cosx%29%5E4%E7%9A%84%E6%9C%80%E5%B0%8F%E6%AD%A3%E5%91%A8%E6%9C%9F3%29%E6%B1%82%E5%87%BD%E6%95%B0y%3D2sinx%28sinx%2Bcosx%29%E7%9A%84%E5%87%8F%E5%8C%BA%E9%97%B41%290.25+2%29%CF%80%2F4+3%29%5Bk%CF%80%2B3%2F8%CF%80%2Ck%CF%80%2B7%2F8%CF%80%5D)
三道关于高一三角函数的题目1)求值cos(π/5)cos(2π/5)2)求函数y=1-(cosx)^2+(cosx)^4的最小正周期3)求函数y=2sinx(sinx+cosx)的减区间1)0.25 2)π/4 3)[kπ+3/8π,kπ+7/8π]
三道关于高一三角函数的题目
1)求值cos(π/5)cos(2π/5)
2)求函数y=1-(cosx)^2+(cosx)^4的最小正周期
3)求函数y=2sinx(sinx+cosx)的减区间
1)0.25 2)π/4 3)[kπ+3/8π,kπ+7/8π]
三道关于高一三角函数的题目1)求值cos(π/5)cos(2π/5)2)求函数y=1-(cosx)^2+(cosx)^4的最小正周期3)求函数y=2sinx(sinx+cosx)的减区间1)0.25 2)π/4 3)[kπ+3/8π,kπ+7/8π]
1)1/4
∵cos(π/5)cos(2π/5)+sin(π/5)sin(2π/5)=cos(π/5)
cos(π/5)cos(2π/5)-sin(π/5)sin(2π/5)=cos(3π/5)
∴cos(π/5)cos(2π/5)=[cos(π/5)+cos(3π/5) ]/2
又∵cos(π/5)+cos(3π/5)=cos(π/5)-cos(2π/5)
cos(π/5)-cos(2π/5)=-cos(4π/5)-cos(2π/5)
cos(π/5)-2cos(π/5)^2+1=-cos(2π/5)-2cos(2π/5)^2+1
cos(π/5)-2cos(π/5)^2=-cos(2π/5)-2cos(2π/5)^2
cos(π/5)+cos(2π/5)=[cos(π/5)^2-cos(2π/5)^2]*2
[cos(π/5)-cos(2π/5)]*2=1
∴cos(π/5)cos(2π/5)=[cos(π/5)+cos(3π/5) ]/2=1/4
2）y=1-(cosx)^2+(cosx)^4
=1+(cosx)^2*[(cosx)^2-1]
=1+(sin2x)^2/4
3）y=2*(sinx)^2+sin2x
=1-cos2x+sin2x
=1- (根号2)*sin(x-π/4)
汗~~~，这也问