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受欢迎的三角函数 >

sin(4x+pi/4)=1

解答

sin (4 x + \frac{π}{4}) = 1

解答

x = \frac{πn}{2} + \frac{π}{16}

+1

度数

x = 11.2 5^{\circ} + 9 0^{\circ} n

求解步骤

sin (4 x + \frac{π}{4}) = 1

sin (4 x + \frac{π}{4}) = 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}

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

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

解

4 x + \frac{π}{4} = \frac{π}{2} + 2 πn : x = \frac{πn}{2} + \frac{π}{16}

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

将

\frac{π}{4}

到右边

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

两边减去

\frac{π}{4}

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

化简

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

化简

4 x + \frac{π}{4} - \frac{π}{4} : 4 x

4 x + \frac{π}{4} - \frac{π}{4}

同类项相加:

\frac{π}{4} - \frac{π}{4} = 0

= 4 x

化简

\frac{π}{2} + 2 πn - \frac{π}{4} : 2 πn + \frac{π}{4}

\frac{π}{2} + 2 πn - \frac{π}{4}

对同类项分组

= 2 πn + \frac{π}{2} - \frac{π}{4}

2, 4

的最小公倍数:

4

2, 4

最小公倍数 (LCM)

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

将每个因子乘以它在

2

或

4

中出现的最多次数

= 2 \cdot 2

数字相乘:

2 \cdot 2 = 4

= 4

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

4

对于

\frac{π}{2} :

将分母和分子乘以

2

\frac{π}{2} = \frac{π 2}{2 \cdot 2} = \frac{π 2}{4}

= \frac{π 2}{4} - \frac{π}{4}

因为分母相等，所以合并分式:

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

= \frac{π 2 - π}{4}

同类项相加:

2 π - π = π

= 2 πn + \frac{π}{4}

4 x = 2 πn + \frac{π}{4}

4 x = 2 πn + \frac{π}{4}

4 x = 2 πn + \frac{π}{4}

两边除以

4

4 x = 2 πn + \frac{π}{4}

两边除以

4

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

化简

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

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{2 πn}{4} + \frac{\frac{π}{4}}{4} : \frac{πn}{2} + \frac{π}{16}

\frac{2 πn}{4} + \frac{\frac{π}{4}}{4}

\frac{2 πn}{4} = \frac{πn}{2}

\frac{2 πn}{4}

约分:

2

= \frac{πn}{2}

\frac{\frac{π}{4}}{4} = \frac{π}{16}

\frac{\frac{π}{4}}{4}

使用分式法则:

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

= \frac{π}{4 \cdot 4}

数字相乘:

4 \cdot 4 = 16

= \frac{π}{16}

= \frac{πn}{2} + \frac{π}{16}

x = \frac{πn}{2} + \frac{π}{16}

x = \frac{πn}{2} + \frac{π}{16}

x = \frac{πn}{2} + \frac{π}{16}

x = \frac{πn}{2} + \frac{π}{16}

作图

流行的例子

cos^2(x)-cos(x)=0,(0,2pi)

cos^{2} (x) - cos (x) = 0, (0, 2 π)

csc (4 2^{\circ}) = sec (x)

solvefor x,0=cos(x)+1+sin(x)

so l v e f or x, 0 = cos (x) + 1 + sin (x)

5 sin (\frac{π}{4} x) = 4

1-sec^2(θ)=tan^2(θ)

1 - sec^{2} (θ) = tan^{2} (θ)