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受欢迎的三角函数 >

2sin(5x)+3=2

解答

2 sin (5 x) + 3 = 2

解答

x = \frac{7 π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

+1

度数

x = 4 2^{\circ} + 7 2^{\circ} n, x = 6 6^{\circ} + 7 2^{\circ} n

求解步骤

2 sin (5 x) + 3 = 2

将

3

到右边

2 sin (5 x) + 3 = 2

两边减去

3

2 sin (5 x) + 3 - 3 = 2 - 3

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{7 π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

5 x = \frac{7 π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

解

5 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{30} + \frac{2 πn}{5}

5 x = \frac{7 π}{6} + 2 πn

两边除以

5

5 x = \frac{7 π}{6} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{7 π}{6}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{7 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{7 π}{6}}{5} + \frac{2 πn}{5} : \frac{7 π}{30} + \frac{2 πn}{5}

\frac{\frac{7 π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{7 π}{6}}{5} = \frac{7 π}{30}

\frac{\frac{7 π}{6}}{5}

使用分式法则:

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

= \frac{7 π}{6 \cdot 5}

数字相乘:

6 \cdot 5 = 30

= \frac{7 π}{30}

= \frac{7 π}{30} + \frac{2 πn}{5}

x = \frac{7 π}{30} + \frac{2 πn}{5}

x = \frac{7 π}{30} + \frac{2 πn}{5}

x = \frac{7 π}{30} + \frac{2 πn}{5}

解

5 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{30} + \frac{2 πn}{5}

5 x = \frac{11 π}{6} + 2 πn

两边除以

5

5 x = \frac{11 π}{6} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{11 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{11 π}{6}}{5} + \frac{2 πn}{5} : \frac{11 π}{30} + \frac{2 πn}{5}

\frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{11 π}{6}}{5} = \frac{11 π}{30}

\frac{\frac{11 π}{6}}{5}

使用分式法则:

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

= \frac{11 π}{6 \cdot 5}

数字相乘:

6 \cdot 5 = 30

= \frac{11 π}{30}

= \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{7 π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

作图

流行的例子

5sin(y)-5=3sin(y)-4

2cos^2(x)+3cos(x)-3=0

3sin(x)-5cos(x)=0

cos(x-60)=(sqrt(3))/2