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受欢迎的三角函数 >

sin(1/2 x)+1=0

解答

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

解答

x = 3 π + 4 πn

+1

度数

x = 54 0^{\circ} + 72 0^{\circ} n

求解步骤

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

将

1

到右边

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

两边减去

1

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

化简

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

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

sin (\frac{1}{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}

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

解

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

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

在两边乘以

2

\frac{1}{2} x = \frac{3 π}{2} + 2 πn

在两边乘以

2

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

化简

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

2 \cdot \frac{3 π}{2} + 2 \cdot 2 πn

2 \cdot \frac{3 π}{2} = 3 π

2 \cdot \frac{3 π}{2}

分式相乘:

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

= \frac{3 π 2}{2}

约分:

2

= 3 π

2 \cdot 2 πn = 4 πn

2 \cdot 2 πn

数字相乘:

2 \cdot 2 = 4

= 4 πn

= 3 π + 4 πn

x = 3 π + 4 πn

x = 3 π + 4 πn

x = 3 π + 4 πn

x = 3 π + 4 πn

作图

流行的例子

4cos^2(x)+8cos(x)+4=0

4 cos^{2} (x) + 8 cos (x) + 4 = 0

4sin(x)cos(x)=2sqrt(2)cos(x)

4 sin (x) cos (x) = 22 cos (x)

sin (x) = \frac{24}{27}

cot^{2} (x) = 0

4cos^2(x)+5sin(x)=3

4 cos^{2} (x) + 5 sin (x) = 3