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受欢迎的三角函数 >

2sin(5x)+sqrt(3)=0,0<= x<= 2pi

解答

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

解答

x = \frac{4 π}{15}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{11 π}{15}, x = \frac{16 π}{15}, x = \frac{17 π}{15}, x = \frac{22 π}{15}, x = \frac{23 π}{15}, x = \frac{28 π}{15}, x = \frac{29 π}{15}

+1

度数

x = 4 8^{\circ}, x = 6 0^{\circ}, x = 12 0^{\circ}, x = 13 2^{\circ}, x = 19 2^{\circ}, x = 20 4^{\circ}, x = 26 4^{\circ}, x = 27 6^{\circ}, x = 33 6^{\circ}, x = 34 8^{\circ}

求解步骤

2 sin (5 x) + 3 = 0, 0 \leq x \leq 2 π

将

3

到右边

2 sin (5 x) + 3 = 0

两边减去

3

2 sin (5 x) + 3 - 3 = 0 - 3

化简

2 sin (5 x) = - 3

2 sin (5 x) = - 3

两边除以

2

2 sin (5 x) = - 3

两边除以

2

\frac{2 sin ( 5 x )}{2} = \frac{- 3}{2}

化简

sin (5 x) = - \frac{3}{2}

sin (5 x) = - \frac{3}{2}

sin (5 x) = - \frac{3}{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{4 π}{3} + 2 πn, 5 x = \frac{5 π}{3} + 2 πn

5 x = \frac{4 π}{3} + 2 πn, 5 x = \frac{5 π}{3} + 2 πn

解

5 x = \frac{4 π}{3} + 2 πn : x = \frac{4 π}{15} + \frac{2 πn}{5}

5 x = \frac{4 π}{3} + 2 πn

两边除以

5

5 x = \frac{4 π}{3} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{4 π}{3}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{4 π}{3}}{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{4 π}{3}}{5} + \frac{2 πn}{5} : \frac{4 π}{15} + \frac{2 πn}{5}

\frac{\frac{4 π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{4 π}{3}}{5} = \frac{4 π}{15}

\frac{\frac{4 π}{3}}{5}

使用分式法则:

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

= \frac{4 π}{3 \cdot 5}

数字相乘:

3 \cdot 5 = 15

= \frac{4 π}{15}

= \frac{4 π}{15} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}

解

5 x = \frac{5 π}{3} + 2 πn : x = \frac{π}{3} + \frac{2 πn}{5}

5 x = \frac{5 π}{3} + 2 πn

两边除以

5

5 x = \frac{5 π}{3} + 2 πn

两边除以

5

\frac{5 x}{5} = \frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

化简

\frac{5 x}{5} = \frac{\frac{5 π}{3}}{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}{3}}{5} + \frac{2 πn}{5} : \frac{π}{3} + \frac{2 πn}{5}

\frac{\frac{5 π}{3}}{5} + \frac{2 πn}{5}

\frac{\frac{5 π}{3}}{5} = \frac{π}{3}

\frac{\frac{5 π}{3}}{5}

使用分式法则:

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

= \frac{5 π}{3 \cdot 5}

数字相乘:

3 \cdot 5 = 15

= \frac{5 π}{15}

约分:

5

= \frac{π}{3}

= \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{π}{3} + \frac{2 πn}{5}

x = \frac{4 π}{15} + \frac{2 πn}{5}, x = \frac{π}{3} + \frac{2 πn}{5}

在

0 \leq x \leq 2 π

范围内的解

x = \frac{4 π}{15}, x = \frac{π}{3}, x = \frac{2 π}{3}, x = \frac{11 π}{15}, x = \frac{16 π}{15}, x = \frac{17 π}{15}, x = \frac{22 π}{15}, x = \frac{23 π}{15}, x = \frac{28 π}{15}, x = \frac{29 π}{15}

作图

流行的例子

sin(2θ)=-24/25

sin (2 θ) = - \frac{24}{25}

sin(4x)+cos(4x)=1

sin (4 x) + cos (4 x) = 1

cos (A) = 0.7865

sin(x)=cos(2x+51)

sin (x) = cos (2 x + 5 1^{\circ})

sin (x) = \frac{π}{4}