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受欢迎的三角函数 >

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

解答

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

解答

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

+1

度数

x = 9 0^{\circ} + 108 0^{\circ} n, x = 99 0^{\circ} + 108 0^{\circ} n

求解步骤

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

将

3

到右边

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

两边加上

3

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

化简

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

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

两边除以

2

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

两边除以

2

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

化简

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

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

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

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

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

解

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

\frac{x}{3} = \frac{π}{6} + 2 πn

在两边乘以

3

\frac{x}{3} = \frac{π}{6} + 2 πn

在两边乘以

3

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

化简

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

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

3 \cdot \frac{π}{6} + 3 \cdot 2 πn : \frac{π}{2} + 6 πn

3 \cdot \frac{π}{6} + 3 \cdot 2 πn

3 \cdot \frac{π}{6} = \frac{π}{2}

3 \cdot \frac{π}{6}

分式相乘:

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

= \frac{π 3}{6}

约分:

3

= \frac{π}{2}

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

数字相乘:

3 \cdot 2 = 6

= 6 πn

= \frac{π}{2} + 6 πn

x = \frac{π}{2} + 6 πn

x = \frac{π}{2} + 6 πn

x = \frac{π}{2} + 6 πn

解

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

\frac{x}{3} = \frac{11 π}{6} + 2 πn

在两边乘以

3

\frac{x}{3} = \frac{11 π}{6} + 2 πn

在两边乘以

3

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

化简

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

化简

\frac{3 x}{3} : x

\frac{3 x}{3}

数字相除:

\frac{3}{3} = 1

= x

化简

3 \cdot \frac{11 π}{6} + 3 \cdot 2 πn : \frac{11 π}{2} + 6 πn

3 \cdot \frac{11 π}{6} + 3 \cdot 2 πn

3 \cdot \frac{11 π}{6} = \frac{11 π}{2}

3 \cdot \frac{11 π}{6}

分式相乘:

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

= \frac{11 π 3}{6}

数字相乘:

11 \cdot 3 = 33

= \frac{33 π}{6}

约分:

3

= \frac{11 π}{2}

3 \cdot 2 πn = 6 πn

3 \cdot 2 πn

数字相乘:

3 \cdot 2 = 6

= 6 πn

= \frac{11 π}{2} + 6 πn

x = \frac{11 π}{2} + 6 πn

x = \frac{11 π}{2} + 6 πn

x = \frac{11 π}{2} + 6 πn

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

作图

流行的例子

2csc^2(x)+3csc(x)-2=0

2 csc^{2} (x) + 3 csc (x) - 2 = 0

2sin^2(x)+3sin(x)+1=0

2 sin^{2} (x) + 3 sin (x) + 1 = 0

cos (\frac{17 π}{6})

2sin^2(x)-sin(x)-1=0

2 sin^{2} (x) - sin (x) - 1 = 0

cos (- \frac{π}{2})