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受欢迎的三角函数 >

2sin(1/2 x)-sqrt(3)=0

解答

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

解答

x = \frac{2 π}{3} + 4 πn, x = \frac{4 π}{3} + 4 πn

+1

度数

x = 12 0^{\circ} + 72 0^{\circ} n, x = 24 0^{\circ} + 72 0^{\circ} n

求解步骤

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

将

3

到右边

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

两边加上

3

2 sin (\frac{1}{2} x) - 3 + 3 = 0 + 3

化简

2 sin (\frac{1}{2} x) = 3

2 sin (\frac{1}{2} x) = 3

两边除以

2

2 sin (\frac{1}{2} x) = 3

两边除以

2

\frac{2 sin ( \frac{1}{2} x )}{2} = \frac{3}{2}

化简

sin (\frac{1}{2} x) = \frac{3}{2}

sin (\frac{1}{2} x) = \frac{3}{2}

sin (\frac{1}{2} x) = \frac{3}{2}

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}

\frac{1}{2} x = \frac{π}{3} + 2 πn, \frac{1}{2} x = \frac{2 π}{3} + 2 πn

\frac{1}{2} x = \frac{π}{3} + 2 πn, \frac{1}{2} x = \frac{2 π}{3} + 2 πn

解

\frac{1}{2} x = \frac{π}{3} + 2 πn : x = \frac{2 π}{3} + 4 πn

\frac{1}{2} x = \frac{π}{3} + 2 πn

在两边乘以

2

\frac{1}{2} x = \frac{π}{3} + 2 πn

在两边乘以

2

2 \cdot \frac{1}{2} x = 2 \cdot \frac{π}{3} + 2 \cdot 2 πn

化简

2 \cdot \frac{1}{2} x = 2 \cdot \frac{π}{3} + 2 \cdot 2 πn

化简

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

分式相乘:

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

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

约分:

2

= x \cdot 1

乘以:

x \cdot 1 = x

= x

化简

2 \cdot \frac{π}{3} + 2 \cdot 2 πn : \frac{2 π}{3} + 4 πn

2 \cdot \frac{π}{3} + 2 \cdot 2 πn

乘

2 \cdot \frac{π}{3} : \frac{2 π}{3}

2 \cdot \frac{π}{3}

分式相乘:

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

= \frac{π 2}{3}

= \frac{2 π}{3} + 2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn

解

\frac{1}{2} x = \frac{2 π}{3} + 2 πn : x = \frac{4 π}{3} + 4 πn

\frac{1}{2} x = \frac{2 π}{3} + 2 πn

在两边乘以

2

\frac{1}{2} x = \frac{2 π}{3} + 2 πn

在两边乘以

2

2 \cdot \frac{1}{2} x = 2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

化简

2 \cdot \frac{1}{2} x = 2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

化简

2 \cdot \frac{1}{2} x : x

2 \cdot \frac{1}{2} x

分式相乘:

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

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

约分:

2

= x \cdot 1

乘以:

x \cdot 1 = x

= x

化简

2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn : \frac{4 π}{3} + 4 πn

2 \cdot \frac{2 π}{3} + 2 \cdot 2 πn

2 \cdot \frac{2 π}{3} = \frac{4 π}{3}

2 \cdot \frac{2 π}{3}

分式相乘:

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

= \frac{2 π 2}{3}

数字相乘:

2 \cdot 2 = 4

= \frac{4 π}{3}

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn, x = \frac{4 π}{3} + 4 πn

作图

流行的例子

sin(2θ)=sqrt(2)cos(θ)

sin (2 θ) = 2 cos (θ)

30=30cos(1/4 (x-5))+15

30 = 30 cos (\frac{1}{4} (x - 5)) + 15

cos (θ) = - 0.07

cos (θ) = - 0.29

tan (a) = \frac{15}{8}