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受欢迎的三角函数 >

17sin(x)+8=sin(x)

解答

17 sin (x) + 8 = 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

17 sin (x) + 8 = sin (x)

用替代法求解

17 sin (x) + 8 = sin (x)

令

: sin (x) = u

17 u + 8 = u

17 u + 8 = u : u = - \frac{1}{2}

17 u + 8 = u

将

8

到右边

17 u + 8 = u

两边减去

8

17 u + 8 - 8 = u - 8

化简

17 u = u - 8

17 u = u - 8

将

u

para o lado esquerdo

17 u = u - 8

两边减去

u

17 u - u = u - 8 - u

化简

16 u = - 8

16 u = - 8

两边除以

16

16 u = - 8

两边除以

16

\frac{16 u}{16} = \frac{- 8}{16}

化简

\frac{16 u}{16} = \frac{- 8}{16}

化简

\frac{16 u}{16} : u

\frac{16 u}{16}

数字相除:

\frac{16}{16} = 1

= u

化简

\frac{- 8}{16} : - \frac{1}{2}

\frac{- 8}{16}

使用分式法则:

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

= - \frac{8}{16}

约分:

8

= - \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

2(sin(x)+1/2)^2+1=3|sin(x)+1/2 |