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受欢迎的三角函数 >

tan^2(x)-9=0

解答

tan^{2} (x) - 9 = 0

解答

x = 1.24904 \dots + πn, x = - 1.24904 \dots + πn

+1

度数

x = 71.56505 \dots^{\circ} + 18 0^{\circ} n, x = - 71.56505 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) - 9 = 0

用替代法求解

tan^{2} (x) - 9 = 0

令

: tan (x) = u

u^{2} - 9 = 0

u^{2} - 9 = 0 : u = 3, u = - 3

u^{2} - 9 = 0

将

9

到右边

u^{2} - 9 = 0

两边加上

9

u^{2} - 9 + 9 = 0 + 9

化简

u^{2} = 9

u^{2} = 9

对于

x^{2} = f (a)

解为

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

u = 9, u = - 9

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

- 9 = - 3

- 9

9 = 3

9

因式分解数字:

9 = 3^{2}

= 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 3

= - 3

u = 3, u = - 3

u = tan (x)

代回

tan (x) = 3, tan (x) = - 3

tan (x) = 3, tan (x) = - 3

tan (x) = 3 : x = arctan (3) + πn

tan (x) = 3

使用反三角函数性质

tan (x) = 3

tan (x) = 3

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (3) + πn

x = arctan (3) + πn

tan (x) = - 3 : x = arctan (- 3) + πn

tan (x) = - 3

使用反三角函数性质

tan (x) = - 3

tan (x) = - 3

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 3) + πn

x = arctan (- 3) + πn

合并所有解

x = arctan (3) + πn, x = arctan (- 3) + πn

以小数形式表示解

x = 1.24904 \dots + πn, x = - 1.24904 \dots + πn

作图

流行的例子

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