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受欢迎的三角函数 >

9sin(x)+4=sin(x)

解答

9 sin (x) + 4 = sin (x)

解答

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度数

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

求解步骤

9 sin (x) + 4 = sin (x)

用替代法求解

9 sin (x) + 4 = sin (x)

令

: sin (x) = u

9 u + 4 = u

9 u + 4 = u : u = - \frac{1}{2}

9 u + 4 = u

将

4

到右边

9 u + 4 = u

两边减去

4

9 u + 4 - 4 = u - 4

化简

9 u = u - 4

9 u = u - 4

将

u

para o lado esquerdo

9 u = u - 4

两边减去

u

9 u - u = u - 4 - u

化简

8 u = - 4

8 u = - 4

两边除以

8

8 u = - 4

两边除以

8

\frac{8 u}{8} = \frac{- 4}{8}

化简

\frac{8 u}{8} = \frac{- 4}{8}

化简

\frac{8 u}{8} : u

\frac{8 u}{8}

数字相除:

\frac{8}{8} = 1

= u

化简

\frac{- 4}{8} : - \frac{1}{2}

\frac{- 4}{8}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{4}{8}

约分:

4

= - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = - \frac{1}{2}

u = sin (x)

代回

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = - \frac{1}{2}

sin (x) = - \frac{1}{2}

的通解

sin (x)

周期表（周期为

2 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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

合并所有解

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

作图

流行的例子

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