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受欢迎的三角函数 >

tan^2(x)=2

解答

tan^{2} (x) = 2

解答

x = 0.95531 \dots + πn, x = - 0.95531 \dots + πn

+1

度数

x = 54.73561 \dots^{\circ} + 18 0^{\circ} n, x = - 54.73561 \dots^{\circ} + 18 0^{\circ} n

求解步骤

tan^{2} (x) = 2

用替代法求解

tan^{2} (x) = 2

令

: tan (x) = u

u^{2} = 2

u^{2} = 2 : u = 2, u = - 2

u^{2} = 2

对于

x^{2} = f (a)

解为

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

u = 2, u = - 2

u = tan (x)

代回

tan (x) = 2, tan (x) = - 2

tan (x) = 2, tan (x) = - 2

tan (x) = 2 : x = arctan (2) + πn

tan (x) = 2

使用反三角函数性质

tan (x) = 2

tan (x) = 2

的通解

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

x = arctan (2) + πn

x = arctan (2) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

tan (x) = - 2

使用反三角函数性质

tan (x) = - 2

tan (x) = - 2

的通解

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

合并所有解

x = arctan (2) + πn, x = arctan (- 2) + πn

以小数形式表示解

x = 0.95531 \dots + πn, x = - 0.95531 \dots + πn

作图

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