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受欢迎的三角函数 >

sin(x/4)=0

解答

sin (\frac{x}{4}) = 0

解答

x = 8 πn, x = 4 π + 8 πn

+1

度数

x = 0^{\circ} + 144 0^{\circ} n, x = 72 0^{\circ} + 144 0^{\circ} n

求解步骤

sin (\frac{x}{4}) = 0

sin (\frac{x}{4}) = 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}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

\frac{x}{4} = 0 + 2 πn, \frac{x}{4} = π + 2 πn

解

\frac{x}{4} = 0 + 2 πn : x = 8 πn

\frac{x}{4} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{x}{4} = 2 πn

在两边乘以

4

\frac{x}{4} = 2 πn

在两边乘以

4

\frac{4 x}{4} = 4 \cdot 2 πn

化简

x = 8 πn

x = 8 πn

解

\frac{x}{4} = π + 2 πn : x = 4 π + 8 πn

\frac{x}{4} = π + 2 πn

在两边乘以

4

\frac{x}{4} = π + 2 πn

在两边乘以

4

\frac{4 x}{4} = 4 π + 4 \cdot 2 πn

化简

x = 4 π + 8 πn

x = 4 π + 8 πn

x = 8 πn, x = 4 π + 8 πn

作图

流行的例子

sin((4pi)/(11))=sin(θ)*sin((7pi)/(11))

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

sin(2x)=2tan(2x)

sin (2 x) = 2 tan (2 x)

-2cos(2θ)+12=4sin(θ)+9

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

sec^2(x)+sec(x)-2=0

sec^{2} (x) + sec (x) - 2 = 0

(cot(x)-1)(2sin(x)+1)=0

(cot (x) - 1) (2 sin (x) + 1) = 0