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2sin(5x)-1=0

解答

2 sin (5 x) - 1 = 0

解答

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{π}{6} + \frac{2 πn}{5}

+1

度数

x = 6^{\circ} + 7 2^{\circ} n, x = 3 0^{\circ} + 7 2^{\circ} n

求解步骤

2 sin (5 x) - 1 = 0

将

1

到右边

2 sin (5 x) - 1 = 0

两边加上

1

2 sin (5 x) - 1 + 1 = 0 + 1

化简

2 sin (5 x) = 1

2 sin (5 x) = 1

两边除以

2

2 sin (5 x) = 1

两边除以

2

\frac{2 sin ( 5 x )}{2} = \frac{1}{2}

化简

sin (5 x) = \frac{1}{2}

sin (5 x) = \frac{1}{2}

sin (5 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}

5 x = \frac{π}{6} + 2 πn, 5 x = \frac{5 π}{6} + 2 πn

5 x = \frac{π}{6} + 2 πn, 5 x = \frac{5 π}{6} + 2 πn

解

5 x = \frac{π}{6} + 2 πn : x = \frac{π}{30} + \frac{2 πn}{5}

5 x = \frac{π}{6} + 2 πn

两边除以

5

5 x = \frac{π}{6} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{\frac{π}{6}}{5} + \frac{2 πn}{5} : \frac{π}{30} + \frac{2 πn}{5}

\frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{6}}{5} = \frac{π}{30}

\frac{\frac{π}{6}}{5}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{6 \cdot 5}

数字相乘:

6 \cdot 5 = 30

= \frac{π}{30}

= \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

解

5 x = \frac{5 π}{6} + 2 πn : x = \frac{π}{6} + \frac{2 πn}{5}

5 x = \frac{5 π}{6} + 2 πn

两边除以

5

5 x = \frac{5 π}{6} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{5 π}{6}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{5 π}{6}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{\frac{5 π}{6}}{5} + \frac{2 πn}{5} : \frac{π}{6} + \frac{2 πn}{5}

\frac{\frac{5 π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{5 π}{6}}{5} = \frac{π}{6}

\frac{\frac{5 π}{6}}{5}

使用分式法则:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{5 π}{6 \cdot 5}

数字相乘:

6 \cdot 5 = 30

= \frac{5 π}{30}

约分:

5

= \frac{π}{6}

= \frac{π}{6} + \frac{2 πn}{5}

x = \frac{π}{6} + \frac{2 πn}{5}

x = \frac{π}{6} + \frac{2 πn}{5}

x = \frac{π}{6} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{π}{6} + \frac{2 πn}{5}

流行的例子

cos(x)=(2.3)/(2.8)

cos (x) = \frac{2.3}{2.8}

3000=5000[cos(pi/(45)(t-6))]

3000 = 5000 [cos (\frac{π}{45} (t - 6))]

2+cos(θ)=5cos(θ)

2 + cos (θ) = 5 cos (θ)

11=12+3.1cos((2pi)/(365)t)

11 = 12 + 3.1 cos (\frac{2 π}{365} t)

solvefor θ,6sin^2(θ)-3=0 求解

θ, 6 sin^{2} (θ) - 3 = 0