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受欢迎的三角函数 >

sin(1/5 x)=0

解答

sin (\frac{1}{5} x) = 0

解答

x = 10 πn, x = 5 π + 10 πn

+1

度数

x = 0^{\circ} + 180 0^{\circ} n, x = 90 0^{\circ} + 180 0^{\circ} n

求解步骤

sin (\frac{1}{5} x) = 0

sin (\frac{1}{5} x) = 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{1}{5} x = 0 + 2 πn, \frac{1}{5} x = π + 2 πn

\frac{1}{5} x = 0 + 2 πn, \frac{1}{5} x = π + 2 πn

解

\frac{1}{5} x = 0 + 2 πn : x = 10 πn

\frac{1}{5} x = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{1}{5} x = 2 πn

在两边乘以

5

\frac{1}{5} x = 2 πn

在两边乘以

5

5 \cdot \frac{1}{5} x = 5 \cdot 2 πn

化简

x = 10 πn

x = 10 πn

解

\frac{1}{5} x = π + 2 πn : x = 5 π + 10 πn

\frac{1}{5} x = π + 2 πn

在两边乘以

5

\frac{1}{5} x = π + 2 πn

在两边乘以

5

5 \cdot \frac{1}{5} x = 5 π + 5 \cdot 2 πn

化简

x = 5 π + 10 πn

x = 5 π + 10 πn

x = 10 πn, x = 5 π + 10 πn

作图

流行的例子

sin(x)= 3/(2sqrt(3))

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

sin(2x)+sin(x)-sin(3x)=0

sin (2 x) + sin (x) - sin (3 x) = 0

tan (x) = \frac{3}{10}

arccos(2x)+arccos(x)= pi/3

arccos (2 x) + arccos (x) = \frac{π}{3}

1.74*sin(40.31)=1.33*sin(θ)

1.74 \cdot sin (40.3 1^{\circ}) = 1.33 \cdot sin (θ)