已知sinθ=0.28且θ小于90度大于180,求sinθ/2,cosθ/2,tanθ/2的值,要详细过程
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![已知sinθ=0.28且θ小于90度大于180,求sinθ/2,cosθ/2,tanθ/2的值,要详细过程](/uploads/image/z/10918243-19-3.jpg?t=%E5%B7%B2%E7%9F%A5sin%CE%B8%3D0.28%E4%B8%94%CE%B8%E5%B0%8F%E4%BA%8E90%E5%BA%A6%E5%A4%A7%E4%BA%8E180%2C%E6%B1%82sin%CE%B8%2F2%2Ccos%CE%B8%2F2%2Ctan%CE%B8%2F2%E7%9A%84%E5%80%BC%2C%E8%A6%81%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B)
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已知sinθ=0.28且θ小于90度大于180,求sinθ/2,cosθ/2,tanθ/2的值,要详细过程
已知sinθ=0.28且θ小于90度大于180,求sinθ/2,cosθ/2,tanθ/2的值,要详细过程
已知sinθ=0.28且θ小于90度大于180,求sinθ/2,cosθ/2,tanθ/2的值,要详细过程
因为θ大于90度小于180,
所以θ/2大于45度小于90,
所以sinθ/2>0,cosθ/2>0,tanθ/2>0,
因为θ大于90小于180,
所以cosθ<0,
而sinθ=0.28=7/25,
所以cosθ=-24/25,
因为cosθ=1-2(sinθ/2)^2=2(cosθ/2)^2-1,
所以sinθ/2=根号[(1-cosθ)/2]=7根号2/10,
cosθ/2=根号[(1+cosθ)/2]=根号2/10,
tanθ/2=(sinθ/2)/(cosθ/2)=7.
Sin[t] = 0.28,
则Cos[t ]= -Sqrt[1-0.28^2]≈0.96,
2Sin[t/2]Cos[t/2] = 0.28,
Cos[t/2]^2-Sin[t/2]^2 = -Sqrt[1-0.28^2],
t/2为锐角,所以
Sin[t/2]>0,Cos[t/2]>0
解得