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 >

(3cos(x)-6sin(x))^2-27sin^2(x)=-9

解答

(3 cos (x) - 6 sin (x))^{2} - 27 sin^{2} (x) = - 9

解答

x = \frac{π}{4} + πn

+1

度数

x = 4 5^{\circ} + 18 0^{\circ} n

求解步骤

(3 cos (x) - 6 sin (x))^{2} - 27 sin^{2} (x) = - 9

两边减去

- 9

9 cos^{2} (x) - 36 cos (x) sin (x) + 9 sin^{2} (x) + 9 = 0

使用三角恒等式改写

9 + 9 cos^{2} (x) + 9 sin^{2} (x) - 36 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)

= 9 + 9 (1 - sin^{2} (x)) + 9 sin^{2} (x) - 36 cos (x) sin (x)

化简

9 + 9 (1 - sin^{2} (x)) + 9 sin^{2} (x) - 36 cos (x) sin (x) : - 36 cos (x) sin (x) + 18

9 + 9 (1 - sin^{2} (x)) + 9 sin^{2} (x) - 36 cos (x) sin (x)

乘开

9 (1 - sin^{2} (x)) : 9 - 9 sin^{2} (x)

9 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 9, b = 1, c = sin^{2} (x)

= 9 \cdot 1 - 9 sin^{2} (x)

数字相乘:

9 \cdot 1 = 9

= 9 - 9 sin^{2} (x)

= 9 + 9 - 9 sin^{2} (x) + 9 sin^{2} (x) - 36 cos (x) sin (x)

化简

9 + 9 - 9 sin^{2} (x) + 9 sin^{2} (x) - 36 cos (x) sin (x) : - 36 cos (x) sin (x) + 18

9 + 9 - 9 sin^{2} (x) + 9 sin^{2} (x) - 36 cos (x) sin (x)

同类项相加:

- 9 sin^{2} (x) + 9 sin^{2} (x) = 0

= 9 + 9 - 36 cos (x) sin (x)

数字相加:

9 + 9 = 18

= - 36 cos (x) sin (x) + 18

= - 36 cos (x) sin (x) + 18

= - 36 cos (x) sin (x) + 18

使用倍角公式:

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

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

= 18 - 36 \cdot \frac{sin ( 2 x )}{2}

18 - 36 \cdot \frac{sin ( 2 x )}{2} = 0

36 \cdot \frac{sin ( 2 x )}{2} = 18 sin (2 x)

36 \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 36}{2}

数字相除:

\frac{36}{2} = 18

= 18 sin (2 x)

18 - 18 sin (2 x) = 0

将

18

到右边

18 - 18 sin (2 x) = 0

两边减去

18

18 - 18 sin (2 x) - 18 = 0 - 18

化简

- 18 sin (2 x) = - 18

- 18 sin (2 x) = - 18

两边除以

- 18

- 18 sin (2 x) = - 18

两边除以

- 18

\frac{- 18 sin ( 2 x )}{- 18} = \frac{- 18}{- 18}

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{π}{2} + 2 πn

2 x = \frac{π}{2} + 2 πn

解

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

2 x = \frac{π}{2} + 2 πn

两边除以

2

2 x = \frac{π}{2} + 2 πn

两边除以

2

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

化简

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

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

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

使用分式法则:

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

= \frac{π}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{π}{4}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数字相除:

\frac{2}{2} = 1

= πn

= \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

作图

流行的例子

3(cos(x)-sin(x))=0

3 (cos (x) - sin (x)) = 0

4tan(x)+4sqrt(3)=0

4 tan (x) + 43 = 0

cos (2 x - 3 0^{\circ}) = 0

sin (5 a) = 0

tan(x)cos(x)sin(x)-1=0

tan (x) cos (x) sin (x) - 1 = 0