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受欢迎的三角函数 >

-4pi^2sin(2pix)=0

解答

- 4 π^{2} sin (2 π x) = 0

解答

x = n, x = \frac{1}{2} + n

+1

度数

x = 0^{\circ}, x = 28.64788 \dots^{\circ}

求解步骤

- 4 π^{2} sin (2 π x) = 0

两边除以

- 4 π^{2}

- 4 π^{2} sin (2 π x) = 0

两边除以

- 4 π^{2}

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

化简

sin (2 π x) = 0

sin (2 π x) = 0

sin (2 π 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}

2 π x = 0 + 2 πn, 2 π x = π + 2 πn

2 π x = 0 + 2 πn, 2 π x = π + 2 πn

解

2 π x = 0 + 2 πn : x = n

2 π x = 0 + 2 πn

0 + 2 πn = 2 πn

2 π x = 2 πn

两边除以

2 π

2 π x = 2 πn

两边除以

2 π

\frac{2 π x}{2 π} = \frac{2 πn}{2 π}

化简

\frac{2 π x}{2 π} = \frac{2 πn}{2 π}

化简

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{π x}{π}

约分:

π

= x

化简

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{πn}{π}

约分:

π

= n

x = n

x = n

x = n

解

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

2 π x = π + 2 πn

两边除以

2 π

2 π x = π + 2 πn

两边除以

2 π

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

化简

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

化简

\frac{2 π x}{2 π} : x

\frac{2 π x}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{π x}{π}

约分:

π

= x

化简

\frac{π}{2 π} + \frac{2 πn}{2 π} : \frac{1}{2} + n

\frac{π}{2 π} + \frac{2 πn}{2 π}

消掉

\frac{π}{2 π} : \frac{1}{2}

\frac{π}{2 π}

约分:

π

= \frac{1}{2}

= \frac{1}{2} + \frac{2 πn}{2 π}

消掉

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

消掉

\frac{2 πn}{2 π} : n

\frac{2 πn}{2 π}

数字相除:

\frac{2}{2} = 1

= \frac{πn}{π}

约分:

π

= n

= n

= \frac{1}{2} + n

x = \frac{1}{2} + n

x = \frac{1}{2} + n

x = \frac{1}{2} + n

x = n, x = \frac{1}{2} + n

作图

流行的例子

6 sin^{2} (θ) = 2

10 tan (θ) + 9 = 0

189.4=100tan^2(45-x/2)

189.4 = 100 tan^{2} (4 5^{\circ} - \frac{x}{2})

20/3 sin(10x)+5cos(10x)=0

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

cos(3x+pi/4)=-(sqrt(3))/2

cos (3 x + \frac{π}{4}) = - \frac{3}{2}