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受欢迎的三角函数 >

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

解答

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

解答

x \in R 无解

求解步骤

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

用替代法求解

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

令

: sin (x) = u

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

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

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

对于

x^{2} = f (a)

解为

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

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

化简

- \frac{1}{2} : i \frac{1}{2}

- \frac{1}{2}

使用根式运算法则:

- a = - 1 a

- \frac{1}{2} = - 1 \frac{1}{2}

= - 1 \frac{1}{2}

使用虚数运算法则:

- 1 = i

= i \frac{1}{2}

化简

- - \frac{1}{2} : - i \frac{1}{2}

- - \frac{1}{2}

化简

- \frac{1}{2} : i \frac{1}{2}

- \frac{1}{2}

使用根式运算法则:

- a = - 1 a

- \frac{1}{2} = - 1 \frac{1}{2}

= - 1 \frac{1}{2}

使用虚数运算法则:

- 1 = i

= i \frac{1}{2}

= - i \frac{1}{2}

u = i \frac{1}{2}, u = - i \frac{1}{2}

u = sin (x)

代回

sin (x) = i \frac{1}{2}, sin (x) = - i \frac{1}{2}

sin (x) = i \frac{1}{2}, sin (x) = - i \frac{1}{2}

sin (x) = i \frac{1}{2} :

无解

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

无解

sin (x) = - i \frac{1}{2} :

无解

sin (x) = - i \frac{1}{2}

无解

合并所有解

x \in R 无解

作图

流行的例子

sin(x/2)-cos(x/2)=0

sin (\frac{x}{2}) - cos (\frac{x}{2}) = 0

2sin^2(x/3)=1,-pi<= ,x<= pi

2 sin^{2} (\frac{x}{3}) = 1, - π \leq, x \leq π

sin (A) = 0.53

2sin(2x)=cos(2x)

2 sin (2 x) = cos (2 x)

0.428=cos(1.57*x-pi)

0.428 = cos (1.57 \cdot x - π)