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受欢迎的三角函数 >

25csc^2(θ)-4=0

解答

25 csc^{2} (θ) - 4 = 0

解答

θ \in R 无解

求解步骤

25 csc^{2} (θ) - 4 = 0

用替代法求解

25 csc^{2} (θ) - 4 = 0

令

: csc (θ) = u

25 u^{2} - 4 = 0

25 u^{2} - 4 = 0 : u = \frac{2}{5}, u = - \frac{2}{5}

25 u^{2} - 4 = 0

将

4

到右边

25 u^{2} - 4 = 0

两边加上

4

25 u^{2} - 4 + 4 = 0 + 4

化简

25 u^{2} = 4

25 u^{2} = 4

两边除以

25

25 u^{2} = 4

两边除以

25

\frac{25 u ^{2}}{25} = \frac{4}{25}

化简

u^{2} = \frac{4}{25}

u^{2} = \frac{4}{25}

对于

x^{2} = f (a)

解为

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

u = \frac{4}{25}, u = - \frac{4}{25}

\frac{4}{25} = \frac{2}{5}

\frac{4}{25}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{4}{25}

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= \frac{4}{5}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{5}

- \frac{4}{25} = - \frac{2}{5}

- \frac{4}{25}

化简

\frac{4}{25} : \frac{2}{5}

\frac{4}{25}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

= \frac{4}{25}

25 = 5

25

因式分解数字:

25 = 5^{2}

= 5^{2}

使用根式运算法则:

n a^{n} = a

5^{2} = 5

= 5

= \frac{4}{5}

4 = 2

4

因式分解数字:

4 = 2^{2}

= 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 2

= \frac{2}{5}

= - \frac{2}{5}

u = \frac{2}{5}, u = - \frac{2}{5}

u = csc (θ)

代回

csc (θ) = \frac{2}{5}, csc (θ) = - \frac{2}{5}

csc (θ) = \frac{2}{5}, csc (θ) = - \frac{2}{5}

csc (θ) = \frac{2}{5} :

无解

csc (θ) = \frac{2}{5}

csc (x) \leq - 1 or csc (x) \geq 1

无解

csc (θ) = - \frac{2}{5} :

无解

csc (θ) = - \frac{2}{5}

csc (x) \leq - 1 or csc (x) \geq 1

无解

合并所有解

θ \in R 无解

作图

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