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受欢迎的三角函数 >

1+sin^2(x)=0

解答

1 + sin^{2} (x) = 0

解答

x \in R 无解

求解步骤

1 + sin^{2} (x) = 0

用替代法求解

1 + sin^{2} (x) = 0

令

: sin (x) = u

1 + u^{2} = 0

1 + u^{2} = 0 : u = i, u = - i

1 + u^{2} = 0

将

1

到右边

1 + u^{2} = 0

两边减去

1

1 + u^{2} - 1 = 0 - 1

化简

u^{2} = - 1

u^{2} = - 1

对于

x^{2} = f (a)

解为

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

u = - 1, u = - - 1

化简

- 1 : i

- 1

使用虚数运算法则:

- 1 = i

= i

化简

- - 1 : - i

- - 1

使用虚数运算法则:

- 1 = i

= - i

u = i, u = - i

u = sin (x)

代回

sin (x) = i, sin (x) = - i

sin (x) = i, sin (x) = - i

sin (x) = i :

无解

sin (x) = i

无解

sin (x) = - i :

无解

sin (x) = - i

无解

合并所有解

x \in R 无解

作图

流行的例子

2sin^2(x)+4cos^2(x)=1

2 sin^{2} (x) + 4 cos^{2} (x) = 1

-sin(θ)= n/2-3

- sin (θ) = \frac{n}{2} - 3

3sin(θ)+2sin^2(θ)=-1,0<= θ<2pi

3 sin (θ) + 2 sin^{2} (θ) = - 1, 0 \leq θ < 2 π

3sin^2(x)+4sin(x)+1=0

3 sin^{2} (x) + 4 sin (x) + 1 = 0

cos (x) = \frac{9}{14}