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受欢迎的三角函数 >

-1/4 sin(x/2)=0

解答

- \frac{1}{4} sin (\frac{x}{2}) = 0

解答

x = 4 πn, x = 2 π + 4 πn

+1

度数

x = 0^{\circ} + 72 0^{\circ} n, x = 36 0^{\circ} + 72 0^{\circ} n

求解步骤

- \frac{1}{4} sin (\frac{x}{2}) = 0

在两边乘以

- 4

- \frac{1}{4} sin (\frac{x}{2}) = 0

在两边乘以

- 4

(- \frac{1}{4} sin (\frac{x}{2})) (- 4) = 0 \cdot (- 4)

化简

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

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

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

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{x}{2} = 0 + 2 πn, \frac{x}{2} = π + 2 πn

\frac{x}{2} = 0 + 2 πn, \frac{x}{2} = π + 2 πn

解

\frac{x}{2} = 0 + 2 πn : x = 4 πn

\frac{x}{2} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{2} = 2 πn

在两边乘以

2

\frac{x}{2} = 2 πn

在两边乘以

2

\frac{2 x}{2} = 2 \cdot 2 πn

化简

x = 4 πn

x = 4 πn

解

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

\frac{x}{2} = π + 2 πn

在两边乘以

2

\frac{x}{2} = π + 2 πn

在两边乘以

2

\frac{2 x}{2} = 2 π + 2 \cdot 2 πn

化简

x = 2 π + 4 πn

x = 2 π + 4 πn

x = 4 πn, x = 2 π + 4 πn

作图

流行的例子

8|sin(pix)-1/4 |+1=7

8 sin (π x) - \frac{1}{4} + 1 = 7

8sin^2(u)+6sin(u)-9=0

8 sin^{2} (u) + 6 sin (u) - 9 = 0

sin (x) = 2 tan (x)

cos (θ) = \frac{1}{5}

sin(x/2)-cos(x)=0

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