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受欢迎的三角函数 >

9sin(x)tan(x)-2tan(x)=0

解答

9 sin (x) tan (x) - 2 tan (x) = 0

解答

x = πn, x = 0.22409 \dots + 2 πn, x = π - 0.22409 \dots + 2 πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = 12.83958 \dots^{\circ} + 36 0^{\circ} n, x = 167.16041 \dots^{\circ} + 36 0^{\circ} n

求解步骤

9 sin (x) tan (x) - 2 tan (x) = 0

分解

9 sin (x) tan (x) - 2 tan (x) : tan (x) (9 sin (x) - 2)

9 sin (x) tan (x) - 2 tan (x)

因式分解出通项

tan (x)

= tan (x) (9 sin (x) - 2)

tan (x) (9 sin (x) - 2) = 0

分别求解每个部分

tan (x) = 0 or 9 sin (x) - 2 = 0

tan (x) = 0 : x = πn

tan (x) = 0

tan (x) = 0

的通解

tan (x)

周期表（周期为

πn

）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

解

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

9 sin (x) - 2 = 0 : x = arcsin (\frac{2}{9}) + 2 πn, x = π - arcsin (\frac{2}{9}) + 2 πn

9 sin (x) - 2 = 0

将

2

到右边

9 sin (x) - 2 = 0

两边加上

2

9 sin (x) - 2 + 2 = 0 + 2

化简

9 sin (x) = 2

9 sin (x) = 2

两边除以

9

9 sin (x) = 2

两边除以

9

\frac{9 sin ( x )}{9} = \frac{2}{9}

化简

sin (x) = \frac{2}{9}

sin (x) = \frac{2}{9}

使用反三角函数性质

sin (x) = \frac{2}{9}

sin (x) = \frac{2}{9}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{2}{9}) + 2 πn, x = π - arcsin (\frac{2}{9}) + 2 πn

x = arcsin (\frac{2}{9}) + 2 πn, x = π - arcsin (\frac{2}{9}) + 2 πn

合并所有解

x = πn, x = arcsin (\frac{2}{9}) + 2 πn, x = π - arcsin (\frac{2}{9}) + 2 πn

以小数形式表示解

x = πn, x = 0.22409 \dots + 2 πn, x = π - 0.22409 \dots + 2 πn

作图

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