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 >

(-4cos(x)+2sin(x))^2+12sin^2(x)=24

解答

(- 4 cos (x) + 2 sin (x))^{2} + 12 sin^{2} (x) = 24

解答

x = \frac{3 π}{4} + πn

+1

度数

x = 13 5^{\circ} + 18 0^{\circ} n

求解步骤

(- 4 cos (x) + 2 sin (x))^{2} + 12 sin^{2} (x) = 24

两边减去

24

16 cos^{2} (x) - 16 cos (x) sin (x) + 16 sin^{2} (x) - 24 = 0

使用三角恒等式改写

- 24 + 16 cos^{2} (x) + 16 sin^{2} (x) - 16 cos (x) sin (x)

使用毕达哥拉斯恒等式:

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

cos^{2} (x) = 1 - sin^{2} (x)

= - 24 + 16 (1 - sin^{2} (x)) + 16 sin^{2} (x) - 16 cos (x) sin (x)

化简

- 24 + 16 (1 - sin^{2} (x)) + 16 sin^{2} (x) - 16 cos (x) sin (x) : - 16 cos (x) sin (x) - 8

- 24 + 16 (1 - sin^{2} (x)) + 16 sin^{2} (x) - 16 cos (x) sin (x)

乘开

16 (1 - sin^{2} (x)) : 16 - 16 sin^{2} (x)

16 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 16, b = 1, c = sin^{2} (x)

= 16 \cdot 1 - 16 sin^{2} (x)

数字相乘:

16 \cdot 1 = 16

= 16 - 16 sin^{2} (x)

= - 24 + 16 - 16 sin^{2} (x) + 16 sin^{2} (x) - 16 cos (x) sin (x)

化简

- 24 + 16 - 16 sin^{2} (x) + 16 sin^{2} (x) - 16 cos (x) sin (x) : - 16 cos (x) sin (x) - 8

- 24 + 16 - 16 sin^{2} (x) + 16 sin^{2} (x) - 16 cos (x) sin (x)

同类项相加:

- 16 sin^{2} (x) + 16 sin^{2} (x) = 0

= - 24 + 16 - 16 cos (x) sin (x)

数字相加/相减:

- 24 + 16 = - 8

= - 16 cos (x) sin (x) - 8

= - 16 cos (x) sin (x) - 8

= - 16 cos (x) sin (x) - 8

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

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

= - 8 - 16 \cdot \frac{sin ( 2 x )}{2}

- 8 - 16 \cdot \frac{sin ( 2 x )}{2} = 0

16 \cdot \frac{sin ( 2 x )}{2} = 8 sin (2 x)

16 \cdot \frac{sin ( 2 x )}{2}

分式相乘:

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

= \frac{sin ( 2 x ) \cdot 16}{2}

数字相除:

\frac{16}{2} = 8

= 8 sin (2 x)

- 8 - 8 sin (2 x) = 0

将

8

到右边

- 8 - 8 sin (2 x) = 0

两边加上

8

- 8 - 8 sin (2 x) + 8 = 0 + 8

化简

- 8 sin (2 x) = 8

- 8 sin (2 x) = 8

两边除以

- 8

- 8 sin (2 x) = 8

两边除以

- 8

\frac{- 8 sin ( 2 x )}{- 8} = \frac{8}{- 8}

化简

sin (2 x) = - 1

sin (2 x) = - 1

sin (2 x) = - 1

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 x = \frac{3 π}{2} + 2 πn

2 x = \frac{3 π}{2} + 2 πn

解

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

2 x = \frac{3 π}{2} + 2 πn

两边除以

2

2 x = \frac{3 π}{2} + 2 πn

两边除以

2

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

化简

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

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

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

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

\frac{\frac{3 π}{2}}{2} = \frac{3 π}{4}

\frac{\frac{3 π}{2}}{2}

使用分式法则:

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

= \frac{3 π}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{3 π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

作图

流行的例子

-arccos(x)+arctan(5/12)=0

- arccos (x) + arctan (\frac{5}{12}) = 0

sqrt(3)cos(x)+sin(x)=1

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

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

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

sin (x) = 0.37

6 sin (x) + 3 = 0