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 >

cos(5x)cos(3x)-sin(5x)sin(3x)=(sqrt(3))/2

解答

cos (5 x) cos (3 x) - sin (5 x) sin (3 x) = \frac{3}{2}

解答

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{11 π}{48} + \frac{πn}{4}

+1

度数

x = 3.7 5^{\circ} + 4 5^{\circ} n, x = 41.2 5^{\circ} + 4 5^{\circ} n

求解步骤

cos (5 x) cos (3 x) - sin (5 x) sin (3 x) = \frac{3}{2}

使用三角恒等式改写

cos (5 x) cos (3 x) - sin (5 x) sin (3 x)

使用角和恒等式:

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

= cos (5 x + 3 x)

cos (5 x + 3 x) = \frac{3}{2}

cos (5 x + 3 x) = \frac{3}{2}

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

5 x + 3 x = \frac{π}{6} + 2 πn, 5 x + 3 x = \frac{11 π}{6} + 2 πn

5 x + 3 x = \frac{π}{6} + 2 πn, 5 x + 3 x = \frac{11 π}{6} + 2 πn

解

5 x + 3 x = \frac{π}{6} + 2 πn : x = \frac{π}{48} + \frac{πn}{4}

5 x + 3 x = \frac{π}{6} + 2 πn

同类项相加:

5 x + 3 x = 8 x

8 x = \frac{π}{6} + 2 πn

两边除以

8

8 x = \frac{π}{6} + 2 πn

两边除以

8

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} = \frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} : x

\frac{8 x}{8}

数字相除:

\frac{8}{8} = 1

= x

化简

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8} : \frac{π}{48} + \frac{πn}{4}

\frac{\frac{π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{π}{6}}{8} = \frac{π}{48}

\frac{\frac{π}{6}}{8}

使用分式法则:

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

= \frac{π}{6 \cdot 8}

数字相乘:

6 \cdot 8 = 48

= \frac{π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

约分:

2

= \frac{πn}{4}

= \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}

解

5 x + 3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{48} + \frac{πn}{4}

5 x + 3 x = \frac{11 π}{6} + 2 πn

同类项相加:

5 x + 3 x = 8 x

8 x = \frac{11 π}{6} + 2 πn

两边除以

8

8 x = \frac{11 π}{6} + 2 πn

两边除以

8

\frac{8 x}{8} = \frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} = \frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8}

化简

\frac{8 x}{8} : x

\frac{8 x}{8}

数字相除:

\frac{8}{8} = 1

= x

化简

\frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8} : \frac{11 π}{48} + \frac{πn}{4}

\frac{\frac{11 π}{6}}{8} + \frac{2 πn}{8}

\frac{\frac{11 π}{6}}{8} = \frac{11 π}{48}

\frac{\frac{11 π}{6}}{8}

使用分式法则:

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

= \frac{11 π}{6 \cdot 8}

数字相乘:

6 \cdot 8 = 48

= \frac{11 π}{48}

\frac{2 πn}{8} = \frac{πn}{4}

\frac{2 πn}{8}

约分:

2

= \frac{πn}{4}

= \frac{11 π}{48} + \frac{πn}{4}

x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{11 π}{48} + \frac{πn}{4}

x = \frac{π}{48} + \frac{πn}{4}, x = \frac{11 π}{48} + \frac{πn}{4}

作图

流行的例子

- 6 sin (2 x) = 0

sin (3 x) - 1 = 0

- sin (θ) = 0

sin (θ) = \frac{1}{6}

4cos(x)=-sin^2(x)+1

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