已知sin^4θ+cos^4θ=5/9,求sin2θ的值
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/08/11 14:19:31
已知sin^4θ+cos^4θ=5/9,求sin2θ的值
我算出来sin^22θ=4/9,可别人得出的是8/9,为什么会是这样?完全不理解,最后答案到底是什么?
我算出来sin^22θ=4/9,可别人得出的是8/9,为什么会是这样?完全不理解,最后答案到底是什么?
![已知sin^4θ+cos^4θ=5/9,求sin2θ的值](/uploads/image/z/4172146-34-6.jpg?t=%E5%B7%B2%E7%9F%A5sin%5E4%CE%B8%2Bcos%5E4%CE%B8%3D5%2F9%2C%E6%B1%82sin2%CE%B8%E7%9A%84%E5%80%BC)
因为 (sin θ)^2 +(cos θ)^2 =1,
且 (sin θ)^4 +(cos θ)^4 =5/9,
所以 1 = [ (sin θ)^2 +(cos θ)^2 ]^2
= (sin θ)^4 +(cos θ)^4 +2 (sin θ)^2 (cos θ)^2
= 5/9 +(1/2) *(2 sin θ cos θ)^2
= 5/9 +(1/2) *(sin 2θ)^2.
解得 sin 2θ = ±2√2 /3.
= = = = = = = = =
注意:
2 (sin θ)^2 (cos θ)^2
= (1/2) *(2 sin θ cos θ)^2
= (1/2) *(sin 2θ)^2.
且 (sin θ)^4 +(cos θ)^4 =5/9,
所以 1 = [ (sin θ)^2 +(cos θ)^2 ]^2
= (sin θ)^4 +(cos θ)^4 +2 (sin θ)^2 (cos θ)^2
= 5/9 +(1/2) *(2 sin θ cos θ)^2
= 5/9 +(1/2) *(sin 2θ)^2.
解得 sin 2θ = ±2√2 /3.
= = = = = = = = =
注意:
2 (sin θ)^2 (cos θ)^2
= (1/2) *(2 sin θ cos θ)^2
= (1/2) *(sin 2θ)^2.
已知sin^4θ+cos^4θ=5/9,求sin2θ的值
已知sin^4θ +cos^4θ=5/9,求sin2θ 的值
已知sinθ的4次方+cosθ的四次方=5/9,求sin2θ的值
已知sin∧4θ+cos∧4θ=5/9,求sin2θ
己知sin^4θ+cos^4θ=5/9,求sin2θ的值
已知sinθ+cosθ=5/4,求sin2θ和sin3θ+cos3θ的值.
已知2cosθ-sinθ=0 求3cos2θ+4sin2θ的值
已知sinθ四次方+cosθ四次方=5/9,求sin2θ的值
已知sinθ-2cosθ=0,求sin2θ-cos2θ/sinθ*cosθ 的值
已知锐角θ满足sin(πcosθ)=cos(πsinθ) 求sin2θ的值?
已知sin^4θ+cos^4θ=5/9,则sin2θ=?
已知sinθ=4/5,且sinθ+cosθ>1,sin2θ=