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受欢迎的三角函数 >

-2sin(2x)= pi/(12)

解答

- 2 sin (2 x) = \frac{π}{12}

解答

x = - \frac{0.13127 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.13127 \dots}{2} + πn

+1

度数

x = - 3.76079 \dots^{\circ} + 18 0^{\circ} n, x = 93.76079 \dots^{\circ} + 18 0^{\circ} n

求解步骤

- 2 sin (2 x) = \frac{π}{12}

两边除以

- 2

- 2 sin (2 x) = \frac{π}{12}

两边除以

- 2

\frac{- 2 sin ( 2 x )}{- 2} = \frac{\frac{π}{12}}{- 2}

化简

\frac{- 2 sin ( 2 x )}{- 2} = \frac{\frac{π}{12}}{- 2}

化简

\frac{- 2 sin ( 2 x )}{- 2} : sin (2 x)

\frac{- 2 sin ( 2 x )}{- 2}

使用分式法则:

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

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

数字相除:

\frac{2}{2} = 1

= sin (2 x)

化简

\frac{\frac{π}{12}}{- 2} : - \frac{π}{24}

\frac{\frac{π}{12}}{- 2}

使用分式法则:

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

= - \frac{\frac{π}{12}}{2}

使用分式法则:

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

\frac{\frac{π}{12}}{2} = \frac{π}{12 \cdot 2}

= - \frac{π}{12 \cdot 2}

数字相乘:

12 \cdot 2 = 24

= - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

使用反三角函数性质

sin (2 x) = - \frac{π}{24}

sin (2 x) = - \frac{π}{24}

的通解

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

2 x = arcsin (- \frac{π}{24}) + 2 πn, 2 x = π + arcsin (\frac{π}{24}) + 2 πn

2 x = arcsin (- \frac{π}{24}) + 2 πn, 2 x = π + arcsin (\frac{π}{24}) + 2 πn

解

2 x = arcsin (- \frac{π}{24}) + 2 πn : x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn

2 x = arcsin (- \frac{π}{24}) + 2 πn

化简

arcsin (- \frac{π}{24}) + 2 πn : - arcsin (\frac{π}{24}) + 2 πn

arcsin (- \frac{π}{24}) + 2 πn

利用以下特性:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{π}{24}) = - arcsin (\frac{π}{24})

= - arcsin (\frac{π}{24}) + 2 πn

2 x = - arcsin (\frac{π}{24}) + 2 πn

两边除以

2

2 x = - arcsin (\frac{π}{24}) + 2 πn

两边除以

2

\frac{2 x}{2} = - \frac{arcsin ( \frac{π}{24} )}{2} + \frac{2 πn}{2}

化简

x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn

x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn

解

2 x = π + arcsin (\frac{π}{24}) + 2 πn : x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

2 x = π + arcsin (\frac{π}{24}) + 2 πn

两边除以

2

2 x = π + arcsin (\frac{π}{24}) + 2 πn

两边除以

2

\frac{2 x}{2} = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + \frac{2 πn}{2}

化简

x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

x = - \frac{arcsin ( \frac{π}{24} )}{2} + πn, x = \frac{π}{2} + \frac{arcsin ( \frac{π}{24} )}{2} + πn

以小数形式表示解

x = - \frac{0.13127 \dots}{2} + πn, x = \frac{π}{2} + \frac{0.13127 \dots}{2} + πn

作图

流行的例子

cos(x)=(sec(x))/4

cos (x) = \frac{sec ( x )}{4}

sin(10x)=sin(10(x+1))

sin (10 x) = sin (10 (x + 1))

sin^2(θ)+3sin(θ)=0

sin^{2} (θ) + 3 sin (θ) = 0

cos (x) = - 0.7962

1.04cos^2(x)+0.102cos(x)-0.935=0

1.04 cos^{2} (x) + 0.102 cos (x) - 0.935 = 0