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受欢迎的三角函数 >

(1/2)sin^2(x)=1

解答

(\frac{1}{2}) sin^{2} (x) = 1

解答

x \in R 无解

求解步骤

(\frac{1}{2}) sin^{2} (x) = 1

用替代法求解

\frac{1}{2} sin^{2} (x) = 1

令

: sin (x) = u

\frac{1}{2} u^{2} = 1

\frac{1}{2} u^{2} = 1 : u = 2, u = - 2

\frac{1}{2} u^{2} = 1

在两边乘以

2

\frac{1}{2} u^{2} = 1

在两边乘以

2

2 \cdot \frac{1}{2} u^{2} = 1 \cdot 2

化简

u^{2} = 2

u^{2} = 2

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = 2, u = - 2

u = sin (x)

代回

sin (x) = 2, sin (x) = - 2

sin (x) = 2, sin (x) = - 2

sin (x) = 2 :

无解

sin (x) = 2

- 1 \leq sin (x) \leq 1

无解

sin (x) = - 2 :

无解

sin (x) = - 2

- 1 \leq sin (x) \leq 1

无解

合并所有解

x \in R 无解

作图

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