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 >

(-6cos(x)+2sin(x))^2+32sin^2(x)=48

解答

(- 6 cos (x) + 2 sin (x))^{2} + 32 sin^{2} (x) = 48

解答

x = \frac{3 π}{4} + πn

+1

度数

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

求解步骤

(- 6 cos (x) + 2 sin (x))^{2} + 32 sin^{2} (x) = 48

两边减去

48

36 cos^{2} (x) - 24 cos (x) sin (x) + 36 sin^{2} (x) - 48 = 0

使用三角恒等式改写

- 48 + 36 cos^{2} (x) + 36 sin^{2} (x) - 24 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)

= - 48 + 36 (1 - sin^{2} (x)) + 36 sin^{2} (x) - 24 cos (x) sin (x)

化简

- 48 + 36 (1 - sin^{2} (x)) + 36 sin^{2} (x) - 24 cos (x) sin (x) : - 24 cos (x) sin (x) - 12

- 48 + 36 (1 - sin^{2} (x)) + 36 sin^{2} (x) - 24 cos (x) sin (x)

乘开

36 (1 - sin^{2} (x)) : 36 - 36 sin^{2} (x)

36 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 36, b = 1, c = sin^{2} (x)

= 36 \cdot 1 - 36 sin^{2} (x)

数字相乘:

36 \cdot 1 = 36

= 36 - 36 sin^{2} (x)

= - 48 + 36 - 36 sin^{2} (x) + 36 sin^{2} (x) - 24 cos (x) sin (x)

化简

- 48 + 36 - 36 sin^{2} (x) + 36 sin^{2} (x) - 24 cos (x) sin (x) : - 24 cos (x) sin (x) - 12

- 48 + 36 - 36 sin^{2} (x) + 36 sin^{2} (x) - 24 cos (x) sin (x)

同类项相加:

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

= - 48 + 36 - 24 cos (x) sin (x)

数字相加/相减:

- 48 + 36 = - 12

= - 24 cos (x) sin (x) - 12

= - 24 cos (x) sin (x) - 12

= - 24 cos (x) sin (x) - 12

使用倍角公式:

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

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

= - 12 - 24 \cdot \frac{sin ( 2 x )}{2}

- 12 - 24 \cdot \frac{sin ( 2 x )}{2} = 0

24 \cdot \frac{sin ( 2 x )}{2} = 12 sin (2 x)

24 \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 24}{2}

数字相除:

\frac{24}{2} = 12

= 12 sin (2 x)

- 12 - 12 sin (2 x) = 0

将

12

到右边

- 12 - 12 sin (2 x) = 0

两边加上

12

- 12 - 12 sin (2 x) + 12 = 0 + 12

化简

- 12 sin (2 x) = 12

- 12 sin (2 x) = 12

两边除以

- 12

- 12 sin (2 x) = 12

两边除以

- 12

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

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

tan(x)csc(x)-2tan(x)=3csc(x)-6

tan (x) csc (x) - 2 tan (x) = 3 csc (x) - 6

10=7cos((pi/6)(t+6))+8

10 = 7 cos ((\frac{π}{6}) (t + 6)) + 8

cos(θ)= 1/(sqrt(6))

cos (θ) = \frac{1}{6}

4tan^2(θ)=-sqrt(3)tan(θ)+tan^2(θ)

4 tan^{2} (θ) = - 3 tan (θ) + tan^{2} (θ)

2sec^2(x)-3tan(x)=11

2 sec^{2} (x) - 3 tan (x) = 11