zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

-2+sin(2θ)=-3/2

解答

- 2 + sin (2 θ) = - \frac{3}{2}

解答

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

+1

度数

θ = 1 5^{\circ} + 18 0^{\circ} n, θ = 7 5^{\circ} + 18 0^{\circ} n

求解步骤

- 2 + sin (2 θ) = - \frac{3}{2}

将

2

到右边

- 2 + sin (2 θ) = - \frac{3}{2}

两边加上

2

- 2 + sin (2 θ) + 2 = - \frac{3}{2} + 2

化简

- 2 + sin (2 θ) + 2 = - \frac{3}{2} + 2

化简

- 2 + sin (2 θ) + 2 : sin (2 θ)

- 2 + sin (2 θ) + 2

同类项相加:

- 2 + 2 = 0

= sin (2 θ)

化简

- \frac{3}{2} + 2 : \frac{1}{2}

- \frac{3}{2} + 2

将项转换为分式:

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

= \frac{2 \cdot 2}{2} - \frac{3}{2}

因为分母相等，所以合并分式:

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

= \frac{2 \cdot 2 - 3}{2}

2 \cdot 2 - 3 = 1

2 \cdot 2 - 3

数字相乘:

2 \cdot 2 = 4

= 4 - 3

数字相减:

4 - 3 = 1

= 1

= \frac{1}{2}

sin (2 θ) = \frac{1}{2}

sin (2 θ) = \frac{1}{2}

sin (2 θ) = \frac{1}{2}

sin (2 θ) = \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}

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

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

解

2 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{12} + πn

2 θ = \frac{π}{6} + 2 πn

两边除以

2

2 θ = \frac{π}{6} + 2 πn

两边除以

2

\frac{2 θ}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

化简

\frac{2 θ}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

化简

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数字相除:

\frac{2}{2} = 1

= θ

化简

\frac{\frac{π}{6}}{2} + \frac{2 πn}{2} : \frac{π}{12} + πn

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

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

使用分式法则:

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

= \frac{π}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= \frac{π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{12} + πn

θ = \frac{π}{12} + πn

θ = \frac{π}{12} + πn

θ = \frac{π}{12} + πn

解

2 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{12} + πn

2 θ = \frac{5 π}{6} + 2 πn

两边除以

2

2 θ = \frac{5 π}{6} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数字相除:

\frac{2}{2} = 1

= θ

化简

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2} : \frac{5 π}{12} + πn

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

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

使用分式法则:

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

= \frac{5 π}{6 \cdot 2}

数字相乘:

6 \cdot 2 = 12

= \frac{5 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

作图

流行的例子

tan (c) = \frac{24}{7}

sin (t) = \frac{- 1}{2}

sin(x+pi/6)+cos(x+pi/3)=cos(2x)

sin (x + \frac{π}{6}) + cos (x + \frac{π}{3}) = cos (2 x)

24sin(2t)-24cos(t)=0

24 sin (2 t) - 24 cos (t) = 0

8^{sin^2(x)}=4^{sin(x)-1/8}

8^{s i n^{2} (x)} = 4^{s i n (x) - \frac{1}{8}}