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受欢迎的三角函数 >

10sin(x)tan(x)+tan(x)=0

解答

10 sin (x) tan (x) + tan (x) = 0

解答

x = πn, x = - 0.10016 \dots + 2 πn, x = π + 0.10016 \dots + 2 πn

+1

度数

x = 0^{\circ} + 18 0^{\circ} n, x = - 5.73917 \dots^{\circ} + 36 0^{\circ} n, x = 185.73917 \dots^{\circ} + 36 0^{\circ} n

求解步骤

10 sin (x) tan (x) + tan (x) = 0

分解

10 sin (x) tan (x) + tan (x) : tan (x) (10 sin (x) + 1)

10 sin (x) tan (x) + tan (x)

因式分解出通项

tan (x)

= tan (x) (10 sin (x) + 1)

tan (x) (10 sin (x) + 1) = 0

分别求解每个部分

tan (x) = 0 or 10 sin (x) + 1 = 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

10 sin (x) + 1 = 0 : x = arcsin (- \frac{1}{10}) + 2 πn, x = π + arcsin (\frac{1}{10}) + 2 πn

10 sin (x) + 1 = 0

将

1

到右边

10 sin (x) + 1 = 0

两边减去

1

10 sin (x) + 1 - 1 = 0 - 1

化简

10 sin (x) = - 1

10 sin (x) = - 1

两边除以

10

10 sin (x) = - 1

两边除以

10

\frac{10 sin ( x )}{10} = \frac{- 1}{10}

化简

sin (x) = - \frac{1}{10}

sin (x) = - \frac{1}{10}

使用反三角函数性质

sin (x) = - \frac{1}{10}

sin (x) = - \frac{1}{10}

的通解

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

x = arcsin (- \frac{1}{10}) + 2 πn, x = π + arcsin (\frac{1}{10}) + 2 πn

x = arcsin (- \frac{1}{10}) + 2 πn, x = π + arcsin (\frac{1}{10}) + 2 πn

合并所有解

x = πn, x = arcsin (- \frac{1}{10}) + 2 πn, x = π + arcsin (\frac{1}{10}) + 2 πn

以小数形式表示解

x = πn, x = - 0.10016 \dots + 2 πn, x = π + 0.10016 \dots + 2 πn

作图

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