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受欢迎的三角函数 >

2sin(2x+15)= 1/2

解答

2 sin (2 x + 15) = \frac{1}{2}

解答

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

+1

度数

x = - 422.47959 \dots^{\circ} + 18 0^{\circ} n, x = - 346.95710 \dots^{\circ} + 18 0^{\circ} n

求解步骤

2 sin (2 x + 15) = \frac{1}{2}

两边除以

2

2 sin (2 x + 15) = \frac{1}{2}

两边除以

2

\frac{2 sin ( 2 x + 15 )}{2} = \frac{\frac{1}{2}}{2}

化简

\frac{2 sin ( 2 x + 15 )}{2} = \frac{\frac{1}{2}}{2}

化简

\frac{2 sin ( 2 x + 15 )}{2} : sin (2 x + 15)

\frac{2 sin ( 2 x + 15 )}{2}

数字相除:

\frac{2}{2} = 1

= sin (2 x + 15)

化简

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

\frac{\frac{1}{2}}{2}

使用分式法则:

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

= \frac{1}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

使用反三角函数性质

sin (2 x + 15) = \frac{1}{4}

sin (2 x + 15) = \frac{1}{4}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn, 2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

解

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn : x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn

将

15

到右边

2 x + 15 = arcsin (\frac{1}{4}) + 2 πn

两边减去

15

2 x + 15 - 15 = arcsin (\frac{1}{4}) + 2 πn - 15

化简

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

两边除以

2

2 x = arcsin (\frac{1}{4}) + 2 πn - 15

两边除以

2

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

化简

\frac{2 x}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

\frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

对同类项分组

= - \frac{15}{2} + \frac{2 πn}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

数字相除:

\frac{2}{2} = 1

= - \frac{15}{2} + πn + \frac{arcsin ( \frac{1}{4} )}{2}

对同类项分组

= πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}

解

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn : x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

将

15

到右边

2 x + 15 = π - arcsin (\frac{1}{4}) + 2 πn

两边减去

15

2 x + 15 - 15 = π - arcsin (\frac{1}{4}) + 2 πn - 15

化简

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

两边除以

2

2 x = π - arcsin (\frac{1}{4}) + 2 πn - 15

两边除以

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

化简

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

\frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

\frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2} - \frac{15}{2}

对同类项分组

= \frac{π}{2} - \frac{15}{2} + \frac{2 πn}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

数字相除:

\frac{2}{2} = 1

= \frac{π}{2} - \frac{15}{2} + πn - \frac{arcsin ( \frac{1}{4} )}{2}

对同类项分组

= πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

x = πn - \frac{15}{2} + \frac{arcsin ( \frac{1}{4} )}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{arcsin ( \frac{1}{4} )}{2}

以小数形式表示解

x = πn - \frac{15}{2} + \frac{0.25268 \dots}{2}, x = πn + \frac{π}{2} - \frac{15}{2} - \frac{0.25268 \dots}{2}

作图

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