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受欢迎的三角函数 >

sqrt(6)=-sqrt(8)cos(3x)

解答

6 = - 8 cos (3 x)

解答

x = \frac{5 π}{18} + \frac{2 πn}{3}, x = \frac{7 π}{18} + \frac{2 πn}{3}

+1

度数

x = 5 0^{\circ} + 12 0^{\circ} n, x = 7 0^{\circ} + 12 0^{\circ} n

求解步骤

6 = - 8 cos (3 x)

交换两边

- 8 cos (3 x) = 6

化简

- 8 : - 22

- 8

8 = 22

8

8

质因数分解:

2^{3}

8

8

除以

28 = 4 \cdot 2

= 2 \cdot 4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2 \cdot 2

2

是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 2

= 2^{3}

= 2^{3}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

= 2^{2} \cdot 2

使用根式运算法则:

n ab = n a n b

= 2 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 22

= - 22

(- 22) cos (3 x) = 6

两边除以

- 22

(- 22) cos (3 x) = 6

两边除以

- 22

\frac{( - 2 2 ) cos ( 3 x )}{- 2 2} = \frac{6}{- 2 2}

化简

\frac{( - 2 2 ) cos ( 3 x )}{- 2 2} = \frac{6}{- 2 2}

化简

\frac{( - 2 2 ) cos ( 3 x )}{- 2 2} : cos (3 x)

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

去除括号:

(- a) = - a

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

使用分式法则:

\frac{- a}{- b} = \frac{a}{b}

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

数字相除:

\frac{2}{2} = 1

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

约分:

2

= cos (3 x)

化简

\frac{6}{- 2 2} : - \frac{3}{2}

\frac{6}{- 2 2}

使用分式法则:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{6}{2 2}

- \frac{6}{2 2}

有理化:

- \frac{3}{2}

- \frac{6}{2 2}

乘以共轭根式

\frac{2}{2}

= - \frac{6 2}{2 2 2}

62 = 23

62

分解整数

6 = 2 \cdot 3

= 2 \cdot 3 2

使用根式运算法则:

n ab = n a n b

2 \cdot 3 = 23

= 232

使用根式运算法则:

a a = a

22 = 2

= 23

222 = 4

222

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

222 = 2 \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} = 2^{1 + \frac{1}{2} + \frac{1}{2}}

= 2^{1 + \frac{1}{2} + \frac{1}{2}}

同类项相加:

\frac{1}{2} + \frac{1}{2} = 2 \cdot \frac{1}{2}

= 2^{1 + 2 \cdot \frac{1}{2}}

2 \cdot \frac{1}{2} = 1

2 \cdot \frac{1}{2}

分式相乘:

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

= \frac{1 \cdot 2}{2}

约分:

2

= 1

= 2^{1 + 1}

数字相加:

1 + 1 = 2

= 2^{2}

2^{2} = 4

= 4

= - \frac{2 3}{4}

约分:

2

= - \frac{3}{2}

= - \frac{3}{2}

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

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

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

cos (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}

3 x = \frac{5 π}{6} + 2 πn, 3 x = \frac{7 π}{6} + 2 πn

3 x = \frac{5 π}{6} + 2 πn, 3 x = \frac{7 π}{6} + 2 πn

解

3 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{18} + \frac{2 πn}{3}

3 x = \frac{5 π}{6} + 2 πn

两边除以

3

3 x = \frac{5 π}{6} + 2 πn

两边除以

3

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

化简

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

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3} : \frac{5 π}{18} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{5 π}{6}}{3} = \frac{5 π}{18}

\frac{\frac{5 π}{6}}{3}

使用分式法则:

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

= \frac{5 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{5 π}{18}

= \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}

解

3 x = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{18} + \frac{2 πn}{3}

3 x = \frac{7 π}{6} + 2 πn

两边除以

3

3 x = \frac{7 π}{6} + 2 πn

两边除以

3

\frac{3 x}{3} = \frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 x}{3} = \frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3}

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

\frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3} : \frac{7 π}{18} + \frac{2 πn}{3}

\frac{\frac{7 π}{6}}{3} + \frac{2 πn}{3}

\frac{\frac{7 π}{6}}{3} = \frac{7 π}{18}

\frac{\frac{7 π}{6}}{3}

使用分式法则:

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

= \frac{7 π}{6 \cdot 3}

数字相乘:

6 \cdot 3 = 18

= \frac{7 π}{18}

= \frac{7 π}{18} + \frac{2 πn}{3}

x = \frac{7 π}{18} + \frac{2 πn}{3}

x = \frac{7 π}{18} + \frac{2 πn}{3}

x = \frac{7 π}{18} + \frac{2 πn}{3}

x = \frac{5 π}{18} + \frac{2 πn}{3}, x = \frac{7 π}{18} + \frac{2 πn}{3}

作图

流行的例子

sin(θ)=0.12,8<= θ<360

sin (θ) = 0.12, 8 \leq θ < 36 0^{\circ}

2cos(7x)-sqrt(3)=0

2 cos (7 x) - 3 = 0

sec(x)-1=0,0<= x<= 2pi

sec (x) - 1 = 0, 0 \leq x \leq 2 π

(sin(95)}{8.95}=\frac{sin(x))/5

\frac{sin ( 9 5 ^{\circ} )}{8.95} = \frac{sin ( x )}{5}

tan(θ)= 2/(2sqrt(3))

tan (θ) = \frac{2}{2 3}