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2sin(x-30)=cos(x-60)

解答

2 sin (x - 3 0^{\circ}) = cos (x - 6 0^{\circ})

解答

x = 6 0^{\circ} + 18 0^{\circ} n

+1

弧度

x = \frac{π}{3} + πn

求解步骤

2 sin (x - 3 0^{\circ}) = cos (x - 6 0^{\circ})

使用三角恒等式改写

2 sin (x - 3 0^{\circ}) = cos (x - 6 0^{\circ})

使用三角恒等式改写

sin (x - 3 0^{\circ})

使用角差恒等式:

sin (s - t) = sin (s) cos (t) - cos (s) sin (t)

= sin (x) cos (3 0^{\circ}) - cos (x) sin (3 0^{\circ})

化简

sin (x) cos (3 0^{\circ}) - cos (x) sin (3 0^{\circ}) : \frac{3}{2} sin (x) - \frac{1}{2} cos (x)

sin (x) cos (3 0^{\circ}) - cos (x) sin (3 0^{\circ})

化简

cos (3 0^{\circ}) : \frac{3}{2}

cos (3 0^{\circ})

使用以下普通恒等式:

cos (3 0^{\circ}) = \frac{3}{2}

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2} sin (x) - sin (3 0^{\circ}) cos (x)

化简

sin (3 0^{\circ}) : \frac{1}{2}

sin (3 0^{\circ})

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{3}{2} sin (x) - \frac{1}{2} cos (x)

= \frac{3}{2} sin (x) - \frac{1}{2} cos (x)

使用角差恒等式:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

= cos (x) cos (6 0^{\circ}) + sin (x) sin (6 0^{\circ})

化简

cos (x) cos (6 0^{\circ}) + sin (x) sin (6 0^{\circ}) : \frac{1}{2} cos (x) + \frac{3}{2} sin (x)

cos (x) cos (6 0^{\circ}) + sin (x) sin (6 0^{\circ})

化简

cos (6 0^{\circ}) : \frac{1}{2}

cos (6 0^{\circ})

使用以下普通恒等式:

cos (6 0^{\circ}) = \frac{1}{2}

cos (x)

周期表（周期为

36 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

= \frac{1}{2} cos (x) + sin (6 0^{\circ}) sin (x)

化简

sin (6 0^{\circ}) : \frac{3}{2}

sin (6 0^{\circ})

使用以下普通恒等式:

sin (6 0^{\circ}) = \frac{3}{2}

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

= \frac{1}{2} cos (x) + \frac{3}{2} sin (x)

= \frac{1}{2} cos (x) + \frac{3}{2} sin (x)

2 (\frac{3}{2} sin (x) - \frac{1}{2} cos (x)) = \frac{1}{2} cos (x) + \frac{3}{2} sin (x)

化简

2 (\frac{3}{2} sin (x) - \frac{1}{2} cos (x)) : 3 sin (x) - cos (x)

2 (\frac{3}{2} sin (x) - \frac{1}{2} cos (x))

使用分配律:

a (b - c) = ab - a c

a = 2, b = \frac{3}{2} sin (x), c = \frac{1}{2} cos (x)

= 2 \cdot \frac{3}{2} sin (x) - 2 \cdot \frac{1}{2} cos (x)

化简

2 \cdot \frac{3}{2} sin (x) - 2 \cdot \frac{1}{2} cos (x) : 3 sin (x) - cos (x)

2 \cdot \frac{3}{2} sin (x) - 2 \cdot \frac{1}{2} cos (x)

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

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

分式相乘:

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

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

约分:

2

= sin (x) 3

2 \cdot \frac{1}{2} cos (x) = cos (x)

2 \cdot \frac{1}{2} cos (x)

分式相乘:

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

= \frac{1 \cdot 2}{2} cos (x)

约分:

2

= cos (x) \cdot 1

乘以:

cos (x) \cdot 1 = cos (x)

= cos (x)

= 3 sin (x) - cos (x)

= 3 sin (x) - cos (x)

3 sin (x) - cos (x) = \frac{1}{2} cos (x) + \frac{3}{2} sin (x)

3 sin (x) - cos (x) = \frac{1}{2} cos (x) + \frac{3}{2} sin (x)

两边减去

\frac{1}{2} cos (x) + \frac{3}{2} sin (x)

3 sin (x) - \frac{3}{2} cos (x) - \frac{3}{2} sin (x) = 0

化简

3 sin (x) - \frac{3}{2} cos (x) - \frac{3}{2} sin (x) : \frac{3 sin ( x ) - 3 cos ( x )}{2}

3 sin (x) - \frac{3}{2} cos (x) - \frac{3}{2} sin (x)

乘

\frac{3}{2} cos (x) : \frac{3 cos ( x )}{2}

\frac{3}{2} cos (x)

分式相乘:

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

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

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

乘

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

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

分式相乘:

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

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

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

合并分式

- \frac{3 cos ( x )}{2} - \frac{3 sin ( x )}{2} : \frac{- 3 cos ( x ) - 3 sin ( x )}{2}

使用法则

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

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

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

将项转换为分式:

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

= \frac{3 sin ( x ) \cdot 2}{2} + \frac{- 3 cos ( x ) - 3 sin ( x )}{2}

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{3 sin ( x ) \cdot 2 - 3 cos ( x ) - 3 sin ( x )}{2}

3 sin (x) \cdot 2 - 3 cos (x) - 3 sin (x) = 3 sin (x) - 3 cos (x)

3 sin (x) \cdot 2 - 3 cos (x) - 3 sin (x)

对同类项分组

= 23 sin (x) - 3 cos (x) - 3 sin (x)

同类项相加:

23 sin (x) - 3 sin (x) = 3 sin (x)

= 3 sin (x) - 3 cos (x)

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

\frac{3 sin ( x ) - 3 cos ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

3 sin (x) - 3 cos (x) = 0

使用三角恒等式改写

3 sin (x) - 3 cos (x) = 0

在两边除以

cos (x), cos (x) \neq = 0

\frac{3 sin ( x ) - 3 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

化简

\frac{3 sin ( x )}{cos ( x )} - 3 = 0

使用基本三角恒等式:

\frac{sin ( x )}{cos ( x )} = tan (x)

3 tan (x) - 3 = 0

3 tan (x) - 3 = 0

将

3

到右边

3 tan (x) - 3 = 0

两边加上

3

3 tan (x) - 3 + 3 = 0 + 3

化简

3 tan (x) = 3

3 tan (x) = 3

两边除以

3

3 tan (x) = 3

两边除以

3

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

化简

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

化简

\frac{3 tan ( x )}{3} : tan (x)

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

约分:

3

= tan (x)

化简

\frac{3}{3} : 3

\frac{3}{3}

使用根式运算法则:

3 = 3^{\frac{1}{2}}

= \frac{3}{3 ^{\frac{1}{2}}}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{3 ^{1}}{3 ^{\frac{1}{2}}} = 3^{1 - \frac{1}{2}}

= 3^{1 - \frac{1}{2}}

数字相减:

1 - \frac{1}{2} = \frac{1}{2}

= 3^{\frac{1}{2}}

使用根式运算法则:

3^{\frac{1}{2}} = 3

= 3

tan (x) = 3

tan (x) = 3

tan (x) = 3

tan (x) = 3

的通解

tan (x)

周期表（周期为

18 0^{\circ} n

）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 6 0^{\circ} + 18 0^{\circ} n

x = 6 0^{\circ} + 18 0^{\circ} n

流行的例子

1 = 2 cos (3 x)

sec (b) = \frac{1}{2}

2cos(2x)=sin(2x)

2 cos (2 x) = sin (2 x)

0.322=sin(3.92232*t)

0.322 = sin (3.92232 \cdot t)

cos(x)tan^2(x)=3cos(x),0<= x<2pi

cos (x) tan^{2} (x) = 3 cos (x), 0 \leq x < 2 π