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受欢迎的三角函数 >

2tan^2(x)=13

解答

2 tan^{2} (x) = 13

解答

x = 1.19700 \dots + πn, x = - 1.19700 \dots + πn

+1

度数

x = 68.58328 \dots^{\circ} + 18 0^{\circ} n, x = - 68.58328 \dots^{\circ} + 18 0^{\circ} n

求解步骤

2 tan^{2} (x) = 13

用替代法求解

2 tan^{2} (x) = 13

令

: tan (x) = u

2 u^{2} = 13

2 u^{2} = 13 : u = \frac{13}{2}, u = - \frac{13}{2}

2 u^{2} = 13

两边除以

2

2 u^{2} = 13

两边除以

2

\frac{2 u ^{2}}{2} = \frac{13}{2}

化简

u^{2} = \frac{13}{2}

u^{2} = \frac{13}{2}

对于

x^{2} = f (a)

解为

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

u = \frac{13}{2}, u = - \frac{13}{2}

u = tan (x)

代回

tan (x) = \frac{13}{2}, tan (x) = - \frac{13}{2}

tan (x) = \frac{13}{2}, tan (x) = - \frac{13}{2}

tan (x) = \frac{13}{2} : x = arctan (\frac{13}{2}) + πn

tan (x) = \frac{13}{2}

使用反三角函数性质

tan (x) = \frac{13}{2}

tan (x) = \frac{13}{2}

的通解

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

x = arctan (\frac{13}{2}) + πn

x = arctan (\frac{13}{2}) + πn

tan (x) = - \frac{13}{2} : x = arctan (- \frac{13}{2}) + πn

tan (x) = - \frac{13}{2}

使用反三角函数性质

tan (x) = - \frac{13}{2}

tan (x) = - \frac{13}{2}

的通解

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

x = arctan (- \frac{13}{2}) + πn

x = arctan (- \frac{13}{2}) + πn

合并所有解

x = arctan (\frac{13}{2}) + πn, x = arctan (- \frac{13}{2}) + πn

以小数形式表示解

x = 1.19700 \dots + πn, x = - 1.19700 \dots + πn

作图

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