两道关于最简三角方程的题目.急啊~~~~~(1)3sin^x+8sinxcosx-3cos^x=5 (2)若对于cita属于R,方程2x^-4xsin(cita)+cos(cita)=0有解,求x满足的条件. 注:^代表平方 要详细过程.谢谢!
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![两道关于最简三角方程的题目.急啊~~~~~(1)3sin^x+8sinxcosx-3cos^x=5 (2)若对于cita属于R,方程2x^-4xsin(cita)+cos(cita)=0有解,求x满足的条件. 注:^代表平方 要详细过程.谢谢!](/uploads/image/z/5245287-15-7.jpg?t=%E4%B8%A4%E9%81%93%E5%85%B3%E4%BA%8E%E6%9C%80%E7%AE%80%E4%B8%89%E8%A7%92%E6%96%B9%E7%A8%8B%E7%9A%84%E9%A2%98%E7%9B%AE.%E6%80%A5%E5%95%8A%EF%BD%9E%EF%BD%9E%EF%BD%9E%EF%BD%9E%EF%BD%9E%EF%BC%881%EF%BC%893sin%5Ex%2B8sinxcosx-3cos%5Ex%3D5+%EF%BC%882%EF%BC%89%E8%8B%A5%E5%AF%B9%E4%BA%8Ecita%E5%B1%9E%E4%BA%8ER%2C%E6%96%B9%E7%A8%8B2x%5E-4xsin%28cita%29%2Bcos%28cita%29%3D0%E6%9C%89%E8%A7%A3%2C%E6%B1%82x%E6%BB%A1%E8%B6%B3%E7%9A%84%E6%9D%A1%E4%BB%B6.+%E6%B3%A8%EF%BC%9A%5E%E4%BB%A3%E8%A1%A8%E5%B9%B3%E6%96%B9+%E8%A6%81%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B.%E8%B0%A2%E8%B0%A2%21)
两道关于最简三角方程的题目.急啊~~~~~(1)3sin^x+8sinxcosx-3cos^x=5 (2)若对于cita属于R,方程2x^-4xsin(cita)+cos(cita)=0有解,求x满足的条件. 注:^代表平方 要详细过程.谢谢!
两道关于最简三角方程的题目.急啊~~~~~
(1)3sin^x+8sinxcosx-3cos^x=5
(2)若对于cita属于R,方程2x^-4xsin(cita)+cos(cita)=0有解,求x满足的条件.
注:^代表平方
要详细过程.谢谢!
两道关于最简三角方程的题目.急啊~~~~~(1)3sin^x+8sinxcosx-3cos^x=5 (2)若对于cita属于R,方程2x^-4xsin(cita)+cos(cita)=0有解,求x满足的条件. 注:^代表平方 要详细过程.谢谢!
3sin^x+8sinxcosx-3cos^x=5
4sin2x-3cos2x=5
4sin2x-3cos2x
1.
∵3sin^x+8sinxcosx-3cos^x=5
∴4sin2x-3cos2x=5
又sin^2x+cos^2x=1
联立解得
sin2x=4/5
cos2x=-3/5
2.△=16sin^θ-8cosθ≥0
16-16cos^θ-8cosθ≥0
解得……
3sin^x+8sinxcosx-3cos^x=5
4sin2x-3cos2x=5
5sin[2x-arctan(3/4)]=5
sin[2x-arctan(3/4)]=1
2x-arctan(3/4)=2kπ+π/2
x=kπ+π/4+[arctan(3/4)]/2
2x^2-4xsinθ+cosθ=0有解
4xsinθ-cosθ=2x...
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3sin^x+8sinxcosx-3cos^x=5
4sin2x-3cos2x=5
5sin[2x-arctan(3/4)]=5
sin[2x-arctan(3/4)]=1
2x-arctan(3/4)=2kπ+π/2
x=kπ+π/4+[arctan(3/4)]/2
2x^2-4xsinθ+cosθ=0有解
4xsinθ-cosθ=2x^2
√(16x^2+1)sin[θ-arctan(1/4x)]=2x^2
sin[θ-arctan(1/4x)]=2x^2/√(16x^2+1)
所以-1<=2x^2/√(16x^2+1)<=1
√(16x^2+1)>0
所以-√(16x^2+1)<=2x^2<=√(16x^2+1)
-√(16x^2+1)<=2x^2一定成立
2x^2<=√(16x^2+1)
4x^4<=16x^2+1
4x^4-16x^2-1<=0
0<=x^2<=(4+√17)/2
所以-√[(4+√17)/2]<=x<=√[(4+√17)/2]
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