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受欢迎的三角函数 >

cos(x)-sin(2x)=cos(3x)-sin(4x)

解答

cos (x) - sin (2 x) = cos (3 x) - sin (4 x)

解答

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn, x = 0.94247 \dots + 2 πn, x = π - 0.94247 \dots + 2 πn, x = - 0.31415 \dots + 2 πn, x = π + 0.31415 \dots + 2 πn

+1

度数

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 5 4^{\circ} + 36 0^{\circ} n, x = 12 6^{\circ} + 36 0^{\circ} n, x = - 1 8^{\circ} + 36 0^{\circ} n, x = 19 8^{\circ} + 36 0^{\circ} n

求解步骤

cos (x) - sin (2 x) = cos (3 x) - sin (4 x)

两边减去

cos (3 x) - sin (4 x)

cos (x) - sin (2 x) - cos (3 x) + sin (4 x) = 0

使用三角恒等式改写

- cos (3 x) + cos (x) - sin (2 x) + sin (4 x)

使用和差化积恒等式:

sin (s) - sin (t) = 2 sin (\frac{s - t}{2}) cos (\frac{s + t}{2})

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

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

2 sin (\frac{4 x - 2 x}{2}) cos (\frac{4 x + 2 x}{2})

\frac{4 x - 2 x}{2} = x

\frac{4 x - 2 x}{2}

同类项相加:

4 x - 2 x = 2 x

= \frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

= 2 sin (x) cos (\frac{4 x + 2 x}{2})

\frac{4 x + 2 x}{2} = 3 x

\frac{4 x + 2 x}{2}

同类项相加:

4 x + 2 x = 6 x

= \frac{6 x}{2}

数字相除:

\frac{6}{2} = 3

= 3 x

= 2 sin (x) cos (3 x)

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

cos (3 x) = 4 cos^{3} (x) - 3 cos (x)

cos (3 x)

使用三角恒等式改写

cos (3 x)

改写为

= cos (2 x + x)

使用角和恒等式:

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

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

使用倍角公式:

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

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

化简

cos (2 x) cos (x) - 2 sin (x) cos (x) sin (x) : cos (x) cos (2 x) - 2 sin^{2} (x) cos (x)

cos (2 x) cos (x) - 2 sin (x) cos (x) sin (x)

2 sin (x) cos (x) sin (x) = 2 sin^{2} (x) cos (x)

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

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

sin (x) sin (x) = sin^{1 + 1} (x)

= 2 cos (x) sin^{1 + 1} (x)

数字相加:

1 + 1 = 2

= 2 cos (x) sin^{2} (x)

= cos (x) cos (2 x) - 2 sin^{2} (x) cos (x)

= cos (x) cos (2 x) - 2 sin^{2} (x) cos (x)

= cos (x) cos (2 x) - 2 sin^{2} (x) cos (x)

使用倍角公式:

cos (2 x) = 2 cos^{2} (x) - 1

= (2 cos^{2} (x) - 1) cos (x) - 2 sin^{2} (x) cos (x)

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

sin^{2} (x) = 1 - cos^{2} (x)

= (2 cos^{2} (x) - 1) cos (x) - 2 (1 - cos^{2} (x)) cos (x)

乘开

(2 cos^{2} (x) - 1) cos (x) - 2 (1 - cos^{2} (x)) cos (x) : 4 cos^{3} (x) - 3 cos (x)

(2 cos^{2} (x) - 1) cos (x) - 2 (1 - cos^{2} (x)) cos (x)

= cos (x) (2 cos^{2} (x) - 1) - 2 cos (x) (1 - cos^{2} (x))

乘开

cos (x) (2 cos^{2} (x) - 1) : 2 cos^{3} (x) - cos (x)

cos (x) (2 cos^{2} (x) - 1)

使用分配律:

a (b - c) = ab - a c

a = cos (x), b = 2 cos^{2} (x), c = 1

= cos (x) 2 cos^{2} (x) - cos (x) 1

= 2 cos^{2} (x) cos (x) - 1 cos (x)

化简

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

2 cos^{2} (x) cos (x) - 1 cos (x)

2 cos^{2} (x) cos (x) = 2 cos^{3} (x)

2 cos^{2} (x) cos (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

cos^{2} (x) cos (x) = cos^{2 + 1} (x)

= 2 cos^{2 + 1} (x)

数字相加:

2 + 1 = 3

= 2 cos^{3} (x)

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

1 cos (x)

乘以:

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

= cos (x)

= 2 cos^{3} (x) - cos (x)

= 2 cos^{3} (x) - cos (x)

= 2 cos^{3} (x) - cos (x) - 2 (1 - cos^{2} (x)) cos (x)

乘开

- 2 cos (x) (1 - cos^{2} (x)) : - 2 cos (x) + 2 cos^{3} (x)

- 2 cos (x) (1 - cos^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = - 2 cos (x), b = 1, c = cos^{2} (x)

= - 2 cos (x) 1 - (- 2 cos (x)) cos^{2} (x)

使用加减运算法则

- (- a) = a

= - 2 \cdot 1 cos (x) + 2 cos^{2} (x) cos (x)

化简

- 2 \cdot 1 \cdot cos (x) + 2 cos^{2} (x) cos (x) : - 2 cos (x) + 2 cos^{3} (x)

- 2 \cdot 1 cos (x) + 2 cos^{2} (x) cos (x)

2 \cdot 1 \cdot cos (x) = 2 cos (x)

2 \cdot 1 cos (x)

数字相乘:

2 \cdot 1 = 2

= 2 cos (x)

2 cos^{2} (x) cos (x) = 2 cos^{3} (x)

2 cos^{2} (x) cos (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

cos^{2} (x) cos (x) = cos^{2 + 1} (x)

= 2 cos^{2 + 1} (x)

数字相加:

2 + 1 = 3

= 2 cos^{3} (x)

= - 2 cos (x) + 2 cos^{3} (x)

= - 2 cos (x) + 2 cos^{3} (x)

= 2 cos^{3} (x) - cos (x) - 2 cos (x) + 2 cos^{3} (x)

化简

2 cos^{3} (x) - cos (x) - 2 cos (x) + 2 cos^{3} (x) : 4 cos^{3} (x) - 3 cos (x)

2 cos^{3} (x) - cos (x) - 2 cos (x) + 2 cos^{3} (x)

对同类项分组

= 2 cos^{3} (x) + 2 cos^{3} (x) - cos (x) - 2 cos (x)

同类项相加:

2 cos^{3} (x) + 2 cos^{3} (x) = 4 cos^{3} (x)

= 4 cos^{3} (x) - cos (x) - 2 cos (x)

同类项相加:

- cos (x) - 2 cos (x) = - 3 cos (x)

= 4 cos^{3} (x) - 3 cos (x)

= 4 cos^{3} (x) - 3 cos (x)

= 4 cos^{3} (x) - 3 cos (x)

= - (4 cos^{3} (x) - 3 cos (x)) + cos (x) + 2 (4 cos^{3} (x) - 3 cos (x)) sin (x)

化简

- (4 cos^{3} (x) - 3 cos (x)) + cos (x) + 2 (4 cos^{3} (x) - 3 cos (x)) sin (x) : - 4 cos^{3} (x) + 4 cos (x) + 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

- (4 cos^{3} (x) - 3 cos (x)) + cos (x) + 2 (4 cos^{3} (x) - 3 cos (x)) sin (x)

= - (4 cos^{3} (x) - 3 cos (x)) + cos (x) + 2 sin (x) (4 cos^{3} (x) - 3 cos (x))

- (4 cos^{3} (x) - 3 cos (x)) : - 4 cos^{3} (x) + 3 cos (x)

- (4 cos^{3} (x) - 3 cos (x))

打开括号

= - (4 cos^{3} (x)) - (- 3 cos (x))

使用加减运算法则

- (- a) = a, - (a) = - a

= - 4 cos^{3} (x) + 3 cos (x)

= - 4 cos^{3} (x) + 3 cos (x) + cos (x) + 2 (4 cos^{3} (x) - 3 cos (x)) sin (x)

乘开

2 sin (x) (4 cos^{3} (x) - 3 cos (x)) : 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

2 sin (x) (4 cos^{3} (x) - 3 cos (x))

使用分配律:

a (b - c) = ab - a c

a = 2 sin (x), b = 4 cos^{3} (x), c = 3 cos (x)

= 2 sin (x) \cdot 4 cos^{3} (x) - 2 sin (x) \cdot 3 cos (x)

= 2 \cdot 4 cos^{3} (x) sin (x) - 2 \cdot 3 sin (x) cos (x)

化简

2 \cdot 4 cos^{3} (x) sin (x) - 2 \cdot 3 sin (x) cos (x) : 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

2 \cdot 4 cos^{3} (x) sin (x) - 2 \cdot 3 sin (x) cos (x)

数字相乘:

2 \cdot 4 = 8

= 8 cos^{3} (x) sin (x) - 2 \cdot 3 sin (x) cos (x)

数字相乘:

2 \cdot 3 = 6

= 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

= 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

= - 4 cos^{3} (x) + 3 cos (x) + cos (x) + 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

同类项相加:

3 cos (x) + cos (x) = 4 cos (x)

= - 4 cos^{3} (x) + 4 cos (x) + 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

= - 4 cos^{3} (x) + 4 cos (x) + 8 cos^{3} (x) sin (x) - 6 sin (x) cos (x)

4 cos (x) - 4 cos^{3} (x) - 6 cos (x) sin (x) + 8 cos^{3} (x) sin (x) = 0

分解

4 cos (x) - 4 cos^{3} (x) - 6 cos (x) sin (x) + 8 cos^{3} (x) sin (x) : 2 cos (x) (2 - 2 cos^{2} (x) - 3 sin (x) + 4 cos^{2} (x) sin (x))

4 cos (x) - 4 cos^{3} (x) - 6 cos (x) sin (x) + 8 cos^{3} (x) sin (x)

使用指数法则:

a^{b + c} = a^{b} a^{c}

sin (x) cos^{3} (x) = cos (x) cos^{2} (x), cos^{3} (x) = cos (x) cos^{2} (x)

= 4 cos (x) - 4 cos (x) cos^{2} (x) - 6 sin (x) cos (x) + 8 cos (x) cos^{2} (x)

将

8

改写为

4 \cdot 2

将

- 6

改写为

3 \cdot 2

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

因式分解出通项

2 cos (x)

= 2 cos (x) (2 - 2 cos^{2} (x) - 3 sin (x) + 4 sin (x) cos^{2} (x))

2 cos (x) (2 - 2 cos^{2} (x) - 3 sin (x) + 4 cos^{2} (x) sin (x)) = 0

分别求解每个部分

cos (x) = 0 or 2 - 2 cos^{2} (x) - 3 sin (x) + 4 cos^{2} (x) sin (x) = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

cos (x) = 0

的通解

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

2 - 2 cos^{2} (x) - 3 sin (x) + 4 cos^{2} (x) sin (x) = 0 : x = 2 πn, x = π + 2 πn, x = arcsin (\frac{1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{1 + 5}{4}) + 2 πn, x = arcsin (\frac{1 - 5}{4}) + 2 πn, x = π + arcsin (- \frac{1 - 5}{4}) + 2 πn

2 - 2 cos^{2} (x) - 3 sin (x) + 4 cos^{2} (x) sin (x) = 0

使用三角恒等式改写

2 - 2 cos^{2} (x) - 3 sin (x) + 4 cos^{2} (x) sin (x)

使用毕达哥拉斯恒等式:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= 2 - 2 (1 - sin^{2} (x)) - 3 sin (x) + 4 (1 - sin^{2} (x)) sin (x)

化简

2 - 2 (1 - sin^{2} (x)) - 3 sin (x) + 4 (1 - sin^{2} (x)) sin (x) : 2 sin^{2} (x) + sin (x) - 4 sin^{3} (x)

2 - 2 (1 - sin^{2} (x)) - 3 sin (x) + 4 (1 - sin^{2} (x)) sin (x)

= 2 - 2 (1 - sin^{2} (x)) - 3 sin (x) + 4 sin (x) (1 - sin^{2} (x))

乘开

- 2 (1 - sin^{2} (x)) : - 2 + 2 sin^{2} (x)

- 2 (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = - 2, b = 1, c = sin^{2} (x)

= - 2 \cdot 1 - (- 2) sin^{2} (x)

使用加减运算法则

- (- a) = a

= - 2 \cdot 1 + 2 sin^{2} (x)

数字相乘:

2 \cdot 1 = 2

= - 2 + 2 sin^{2} (x)

= 2 - 2 + 2 sin^{2} (x) - 3 sin (x) + 4 (1 - sin^{2} (x)) sin (x)

乘开

4 sin (x) (1 - sin^{2} (x)) : 4 sin (x) - 4 sin^{3} (x)

4 sin (x) (1 - sin^{2} (x))

使用分配律:

a (b - c) = ab - a c

a = 4 sin (x), b = 1, c = sin^{2} (x)

= 4 sin (x) \cdot 1 - 4 sin (x) sin^{2} (x)

= 4 \cdot 1 \cdot sin (x) - 4 sin^{2} (x) sin (x)

化简

4 \cdot 1 \cdot sin (x) - 4 sin^{2} (x) sin (x) : 4 sin (x) - 4 sin^{3} (x)

4 \cdot 1 \cdot sin (x) - 4 sin^{2} (x) sin (x)

4 \cdot 1 \cdot sin (x) = 4 sin (x)

4 \cdot 1 \cdot sin (x)

数字相乘:

4 \cdot 1 = 4

= 4 sin (x)

4 sin^{2} (x) sin (x) = 4 sin^{3} (x)

4 sin^{2} (x) sin (x)

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

sin^{2} (x) sin (x) = sin^{2 + 1} (x)

= 4 sin^{2 + 1} (x)

数字相加:

2 + 1 = 3

= 4 sin^{3} (x)

= 4 sin (x) - 4 sin^{3} (x)

= 4 sin (x) - 4 sin^{3} (x)

= 2 - 2 + 2 sin^{2} (x) - 3 sin (x) + 4 sin (x) - 4 sin^{3} (x)

化简

2 - 2 + 2 sin^{2} (x) - 3 sin (x) + 4 sin (x) - 4 sin^{3} (x) : 2 sin^{2} (x) + sin (x) - 4 sin^{3} (x)

2 - 2 + 2 sin^{2} (x) - 3 sin (x) + 4 sin (x) - 4 sin^{3} (x)

同类项相加:

- 3 sin (x) + 4 sin (x) = sin (x)

= 2 - 2 + 2 sin^{2} (x) + sin (x) - 4 sin^{3} (x)

2 - 2 = 0

= 2 sin^{2} (x) + sin (x) - 4 sin^{3} (x)

= 2 sin^{2} (x) + sin (x) - 4 sin^{3} (x)

= 2 sin^{2} (x) + sin (x) - 4 sin^{3} (x)

sin (x) + 2 sin^{2} (x) - 4 sin^{3} (x) = 0

用替代法求解

sin (x) + 2 sin^{2} (x) - 4 sin^{3} (x) = 0

令

: sin (x) = u

u + 2 u^{2} - 4 u^{3} = 0

u + 2 u^{2} - 4 u^{3} = 0 : u = 0, u = \frac{1 + 5}{4}, u = \frac{1 - 5}{4}

u + 2 u^{2} - 4 u^{3} = 0

因式分解

u + 2 u^{2} - 4 u^{3} : - u (4 u^{2} - 2 u - 1)

u + 2 u^{2} - 4 u^{3}

使用指数法则:

a^{b + c} = a^{b} a^{c}

u^{2} = uu

= - 4 u^{2} u + 2 uu + u

因式分解出通项

- u

= - u (4 u^{2} - 2 u - 1)

- u (4 u^{2} - 2 u - 1) = 0

使用零因数法则： If

ab = 0

then

a = 0

or

b = 0

u = 0 or 4 u^{2} - 2 u - 1 = 0

解

4 u^{2} - 2 u - 1 = 0 : u = \frac{1 + 5}{4}, u = \frac{1 - 5}{4}

4 u^{2} - 2 u - 1 = 0

使用求根公式求解

4 u^{2} - 2 u - 1 = 0

二次方程求根公式:

若

a = 4, b = - 2, c = - 1

u_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 4 ( - 1 )}{2 \cdot 4}

u_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 4 ( - 1 )}{2 \cdot 4}

(- 2)^{2} - 4 \cdot 4 (- 1) = 25

(- 2)^{2} - 4 \cdot 4 (- 1)

使用法则

- (- a) = a

= (- 2)^{2} + 4 \cdot 4 \cdot 1

使用指数法则:

(- a)^{n} = a^{n},

若

n

是偶数

(- 2)^{2} = 2^{2}

= 2^{2} + 4 \cdot 4 \cdot 1

数字相乘:

4 \cdot 4 \cdot 1 = 16

= 2^{2} + 16

2^{2} = 4

= 4 + 16

数字相加:

4 + 16 = 20

= 20

20

质因数分解:

2^{2} \cdot 5

20

20

除以

220 = 10 \cdot 2

= 2 \cdot 10

10

除以

210 = 5 \cdot 2

= 2 \cdot 2 \cdot 5

2, 5

都是质数，因此无法进一步因数分解

= 2 \cdot 2 \cdot 5

= 2^{2} \cdot 5

= 2^{2} \cdot 5

使用根式运算法则:

n ab = n a n b

= 5 2^{2}

使用根式运算法则:

n a^{n} = a

2^{2} = 2

= 25

u_{1, 2} = \frac{- ( - 2 ) \pm 2 5}{2 \cdot 4}

将解分隔开

u_{1} = \frac{- ( - 2 ) + 2 5}{2 \cdot 4}, u_{2} = \frac{- ( - 2 ) - 2 5}{2 \cdot 4}

u = \frac{- ( - 2 ) + 2 5}{2 \cdot 4} : \frac{1 + 5}{4}

\frac{- ( - 2 ) + 2 5}{2 \cdot 4}

使用法则

- (- a) = a

= \frac{2 + 2 5}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{2 + 2 5}{8}

分解

2 + 25 : 2 (1 + 5)

2 + 25

改写为

= 2 \cdot 1 + 25

因式分解出通项

2

= 2 (1 + 5)

= \frac{2 ( 1 + 5 )}{8}

约分:

2

= \frac{1 + 5}{4}

u = \frac{- ( - 2 ) - 2 5}{2 \cdot 4} : \frac{1 - 5}{4}

\frac{- ( - 2 ) - 2 5}{2 \cdot 4}

使用法则

- (- a) = a

= \frac{2 - 2 5}{2 \cdot 4}

数字相乘:

2 \cdot 4 = 8

= \frac{2 - 2 5}{8}

分解

2 - 25 : 2 (1 - 5)

2 - 25

改写为

= 2 \cdot 1 - 25

因式分解出通项

2

= 2 (1 - 5)

= \frac{2 ( 1 - 5 )}{8}

约分:

2

= \frac{1 - 5}{4}

二次方程组的解是:

u = \frac{1 + 5}{4}, u = \frac{1 - 5}{4}

解为

u = 0, u = \frac{1 + 5}{4}, u = \frac{1 - 5}{4}

u = sin (x)

代回

sin (x) = 0, sin (x) = \frac{1 + 5}{4}, sin (x) = \frac{1 - 5}{4}

sin (x) = 0, sin (x) = \frac{1 + 5}{4}, sin (x) = \frac{1 - 5}{4}

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

sin (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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

sin (x) = \frac{1 + 5}{4} : x = arcsin (\frac{1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{1 + 5}{4}) + 2 πn

sin (x) = \frac{1 + 5}{4}

使用反三角函数性质

sin (x) = \frac{1 + 5}{4}

sin (x) = \frac{1 + 5}{4}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{1 + 5}{4}) + 2 πn

x = arcsin (\frac{1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{1 + 5}{4}) + 2 πn

sin (x) = \frac{1 - 5}{4} : x = arcsin (\frac{1 - 5}{4}) + 2 πn, x = π + arcsin (- \frac{1 - 5}{4}) + 2 πn

sin (x) = \frac{1 - 5}{4}

使用反三角函数性质

sin (x) = \frac{1 - 5}{4}

sin (x) = \frac{1 - 5}{4}

的通解

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (\frac{1 - 5}{4}) + 2 πn, x = π + arcsin (- \frac{1 - 5}{4}) + 2 πn

x = arcsin (\frac{1 - 5}{4}) + 2 πn, x = π + arcsin (- \frac{1 - 5}{4}) + 2 πn

合并所有解

x = 2 πn, x = π + 2 πn, x = arcsin (\frac{1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{1 + 5}{4}) + 2 πn, x = arcsin (\frac{1 - 5}{4}) + 2 πn, x = π + arcsin (- \frac{1 - 5}{4}) + 2 πn

合并所有解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn, x = arcsin (\frac{1 + 5}{4}) + 2 πn, x = π - arcsin (\frac{1 + 5}{4}) + 2 πn, x = arcsin (\frac{1 - 5}{4}) + 2 πn, x = π + arcsin (- \frac{1 - 5}{4}) + 2 πn

以小数形式表示解

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = 2 πn, x = π + 2 πn, x = 0.94247 \dots + 2 πn, x = π - 0.94247 \dots + 2 πn, x = - 0.31415 \dots + 2 πn, x = π + 0.31415 \dots + 2 πn

作图

流行的例子

cos^2(θ)=2+2sin(θ)

cos^{2} (θ) = 2 + 2 sin (θ)

cos(x)-2cos(x)sin(x)=0

cos (x) - 2 cos (x) sin (x) = 0

2 sec^{2} (x) = 0

2 cos (3 θ) = - 1

1 + sin (2 x) = 0