Question

已知sin^4θ+cos^4θ=5/9,求sin2θ的值

急需过程~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，希望能有人详细的写一下过程，最后答案到底是什么？

Answer 1

解：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.