zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的三角函数 >

sin(3x+10)=cos(x+24)

解答

sin (3 x + 10) = cos (x + 2 4^{\circ})

解答

x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}, x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

+1

弧度

x = \frac{\frac{11 π}{5}}{24} - \frac{5}{2} + \frac{60 π}{120} n, x = - 5 + \frac{\frac{19 π}{5}}{12} + \frac{60 π}{60} n

求解步骤

sin (3 x + 10) = cos (x + 2 4^{\circ})

使用三角恒等式改写

sin (3 x + 10) = cos (x + 2 4^{\circ})

利用以下特性:

cos (x) = sin (9 0^{\circ} - x)

sin (3 x + 10) = sin (9 0^{\circ} - (x + 2 4^{\circ}))

sin (3 x + 10) = sin (9 0^{\circ} - (x + 2 4^{\circ}))

使用反三角函数性质

sin (3 x + 10) = sin (9 0^{\circ} - (x + 2 4^{\circ}))

sin (x) = sin (y) \Rightarrow x = y + 2 π n, x = π - y + 2 π n

3 x + 10 = 9 0^{\circ} - (x + 2 4^{\circ}) + 36 0^{\circ} n, 3 x + 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 2 4^{\circ})) + 36 0^{\circ} n

3 x + 10 = 9 0^{\circ} - (x + 2 4^{\circ}) + 36 0^{\circ} n, 3 x + 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 2 4^{\circ})) + 36 0^{\circ} n

3 x + 10 = 9 0^{\circ} - (x + 2 4^{\circ}) + 36 0^{\circ} n : x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}

3 x + 10 = 9 0^{\circ} - (x + 2 4^{\circ}) + 36 0^{\circ} n

展开

9 0^{\circ} - (x + 2 4^{\circ}) + 36 0^{\circ} n : - x + 36 0^{\circ} n + 6 6^{\circ}

9 0^{\circ} - (x + 2 4^{\circ}) + 36 0^{\circ} n

- (x + 2 4^{\circ}) : - x - 2 4^{\circ}

- (x + 2 4^{\circ})

打开括号

= - (x) - (2 4^{\circ})

使用加减运算法则

+ (- a) = - a

= - x - 2 4^{\circ}

= 9 0^{\circ} - x - 2 4^{\circ} + 36 0^{\circ} n

化简

9 0^{\circ} - x - 2 4^{\circ} + 36 0^{\circ} n : - x + 36 0^{\circ} n + 6 6^{\circ}

9 0^{\circ} - x - 2 4^{\circ} + 36 0^{\circ} n

对同类项分组

= - x + 36 0^{\circ} n + 9 0^{\circ} - 2 4^{\circ}

2, 15

的最小公倍数:

30

2, 15

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

15

质因数分解:

3 \cdot 5

15

15

除以

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

都是质数，因此无法进一步因数分解

= 3 \cdot 5

将每个因子乘以它在

2

或

15

中出现的最多次数

= 2 \cdot 3 \cdot 5

数字相乘:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

对于

9 0^{\circ} :

将分母和分子乘以

15

9 0^{\circ} = \frac{18 0 ^{\circ} 15}{2 \cdot 15} = 9 0^{\circ}

对于

2 4^{\circ} :

将分母和分子乘以

2

2 4^{\circ} = \frac{36 0 ^{\circ} 2}{15 \cdot 2} = 2 4^{\circ}

= 9 0^{\circ} - 2 4^{\circ}

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{18 0 ^{\circ} 15 - 72 0 ^{\circ}}{30}

同类项相加:

270 0^{\circ} - 72 0^{\circ} = 198 0^{\circ}

= - x + 36 0^{\circ} n + 6 6^{\circ}

= - x + 36 0^{\circ} n + 6 6^{\circ}

3 x + 10 = - x + 36 0^{\circ} n + 6 6^{\circ}

将

10

到右边

3 x + 10 = - x + 36 0^{\circ} n + 6 6^{\circ}

两边减去

10

3 x + 10 - 10 = - x + 36 0^{\circ} n + 6 6^{\circ} - 10

化简

3 x = - x + 36 0^{\circ} n + 6 6^{\circ} - 10

3 x = - x + 36 0^{\circ} n + 6 6^{\circ} - 10

将

x

para o lado esquerdo

3 x = - x + 36 0^{\circ} n + 6 6^{\circ} - 10

两边加上

x

3 x + x = - x + 36 0^{\circ} n + 6 6^{\circ} - 10 + x

化简

4 x = 36 0^{\circ} n + 6 6^{\circ} - 10

4 x = 36 0^{\circ} n + 6 6^{\circ} - 10

两边除以

4

4 x = 36 0^{\circ} n + 6 6^{\circ} - 10

两边除以

4

\frac{4 x}{4} = \frac{36 0 ^{\circ} n}{4} + \frac{6 6 ^{\circ}}{4} - \frac{10}{4}

化简

\frac{4 x}{4} = \frac{36 0 ^{\circ} n}{4} + \frac{6 6 ^{\circ}}{4} - \frac{10}{4}

化简

\frac{4 x}{4} : x

\frac{4 x}{4}

数字相除:

\frac{4}{4} = 1

= x

化简

\frac{36 0 ^{\circ} n}{4} + \frac{6 6 ^{\circ}}{4} - \frac{10}{4} : \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}

\frac{36 0 ^{\circ} n}{4} + \frac{6 6 ^{\circ}}{4} - \frac{10}{4}

使用法则

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

= \frac{36 0 ^{\circ} n + 6 6 ^{\circ} - 10}{4}

化简

36 0^{\circ} n + 6 6^{\circ} - 10 : \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{30}

36 0^{\circ} n + 6 6^{\circ} - 10

将项转换为分式:

36 0^{\circ} n = \frac{36 0 ^{\circ} n 30}{30}, 10 = \frac{10 \cdot 30}{30}

= \frac{36 0 ^{\circ} n \cdot 30}{30} + 6 6^{\circ} - \frac{10 \cdot 30}{30}

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{36 0 ^{\circ} n \cdot 30 + 198 0 ^{\circ} - 10 \cdot 30}{30}

36 0^{\circ} n \cdot 30 + 198 0^{\circ} - 10 \cdot 30 = 1080 0^{\circ} n + 198 0^{\circ} - 300

36 0^{\circ} n \cdot 30 + 198 0^{\circ} - 10 \cdot 30

数字相乘:

2 \cdot 30 = 60

= 1080 0^{\circ} n + 198 0^{\circ} - 10 \cdot 30

数字相乘:

10 \cdot 30 = 300

= 1080 0^{\circ} n + 198 0^{\circ} - 300

= \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{30}

= \frac{\frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{30}}{4}

使用分式法则:

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

= \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{30 \cdot 4}

数字相乘:

30 \cdot 4 = 120

= \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}

x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}

x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}

x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}

3 x + 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 2 4^{\circ})) + 36 0^{\circ} n : x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

3 x + 10 = 18 0^{\circ} - (9 0^{\circ} - (x + 2 4^{\circ})) + 36 0^{\circ} n

展开

18 0^{\circ} - (9 0^{\circ} - (x + 2 4^{\circ})) + 36 0^{\circ} n : 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - (x + 2 4^{\circ})) + 36 0^{\circ} n

乘开

9 0^{\circ} - (x + 2 4^{\circ}) : - x + 6 6^{\circ}

9 0^{\circ} - (x + 2 4^{\circ})

- (x + 2 4^{\circ}) : - x - 2 4^{\circ}

- (x + 2 4^{\circ})

打开括号

= - (x) - (2 4^{\circ})

使用加减运算法则

+ (- a) = - a

= - x - 2 4^{\circ}

= 9 0^{\circ} - x - 2 4^{\circ}

化简

9 0^{\circ} - x - 2 4^{\circ} : - x + 6 6^{\circ}

9 0^{\circ} - x - 2 4^{\circ}

对同类项分组

= - x + 9 0^{\circ} - 2 4^{\circ}

2, 15

的最小公倍数:

30

2, 15

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

15

质因数分解:

3 \cdot 5

15

15

除以

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

都是质数，因此无法进一步因数分解

= 3 \cdot 5

将每个因子乘以它在

2

或

15

中出现的最多次数

= 2 \cdot 3 \cdot 5

数字相乘:

2 \cdot 3 \cdot 5 = 30

= 30

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

30

对于

9 0^{\circ} :

将分母和分子乘以

15

9 0^{\circ} = \frac{18 0 ^{\circ} 15}{2 \cdot 15} = 9 0^{\circ}

对于

2 4^{\circ} :

将分母和分子乘以

2

2 4^{\circ} = \frac{36 0 ^{\circ} 2}{15 \cdot 2} = 2 4^{\circ}

= 9 0^{\circ} - 2 4^{\circ}

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{18 0 ^{\circ} 15 - 72 0 ^{\circ}}{30}

同类项相加:

270 0^{\circ} - 72 0^{\circ} = 198 0^{\circ}

= - x + 6 6^{\circ}

= - x + 6 6^{\circ}

= 18 0^{\circ} - (- x + 6 6^{\circ}) + 36 0^{\circ} n

- (- x + 6 6^{\circ}) : x - 6 6^{\circ}

- (- x + 6 6^{\circ})

打开括号

= - (- x) - (6 6^{\circ})

使用加减运算法则

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

= x - 6 6^{\circ}

= 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n

3 x + 10 = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n

将

10

到右边

3 x + 10 = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n

两边减去

10

3 x + 10 - 10 = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n - 10

化简

3 x = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n - 10

3 x = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n - 10

将

x

para o lado esquerdo

3 x = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n - 10

两边减去

x

3 x - x = 18 0^{\circ} + x - 6 6^{\circ} + 36 0^{\circ} n - 10 - x

化简

2 x = 18 0^{\circ} - 6 6^{\circ} + 36 0^{\circ} n - 10

2 x = 18 0^{\circ} - 6 6^{\circ} + 36 0^{\circ} n - 10

两边除以

2

2 x = 18 0^{\circ} - 6 6^{\circ} + 36 0^{\circ} n - 10

两边除以

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{6 6 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{10}{2}

化简

\frac{2 x}{2} = 9 0^{\circ} - \frac{6 6 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{10}{2}

化简

\frac{2 x}{2} : x

\frac{2 x}{2}

数字相除:

\frac{2}{2} = 1

= x

化简

9 0^{\circ} - \frac{6 6 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{10}{2} : \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

9 0^{\circ} - \frac{6 6 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{10}{2}

对同类项分组

= 9 0^{\circ} - \frac{10}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{6 6 ^{\circ}}{2}

使用法则

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

= \frac{18 0 ^{\circ} - 10 + 36 0 ^{\circ} n - 6 6 ^{\circ}}{2}

化简

18 0^{\circ} - 10 + 36 0^{\circ} n - 6 6^{\circ} : \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{30}

18 0^{\circ} - 10 + 36 0^{\circ} n - 6 6^{\circ}

将项转换为分式:

18 0^{\circ} = 18 0^{\circ}, 10 = \frac{10 \cdot 30}{30}, 36 0^{\circ} n = \frac{36 0 ^{\circ} n 30}{30}

= 18 0^{\circ} - \frac{10 \cdot 30}{30} + \frac{36 0 ^{\circ} n \cdot 30}{30} - 6 6^{\circ}

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{18 0 ^{\circ} 30 - 10 \cdot 30 + 36 0 ^{\circ} n \cdot 30 - 198 0 ^{\circ}}{30}

18 0^{\circ} 30 - 10 \cdot 30 + 36 0^{\circ} n \cdot 30 - 198 0^{\circ} = 342 0^{\circ} + 1080 0^{\circ} n - 300

18 0^{\circ} 30 - 10 \cdot 30 + 36 0^{\circ} n \cdot 30 - 198 0^{\circ}

对同类项分组

= 540 0^{\circ} - 198 0^{\circ} + 2 \cdot 540 0^{\circ} n - 10 \cdot 30

同类项相加:

540 0^{\circ} - 198 0^{\circ} = 342 0^{\circ}

= 342 0^{\circ} + 2 \cdot 540 0^{\circ} n - 10 \cdot 30

数字相乘:

2 \cdot 30 = 60

= 342 0^{\circ} + 1080 0^{\circ} n - 10 \cdot 30

数字相乘:

10 \cdot 30 = 300

= 342 0^{\circ} + 1080 0^{\circ} n - 300

= \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{30}

= \frac{\frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{30}}{2}

使用分式法则:

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

= \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{30 \cdot 2}

数字相乘:

30 \cdot 2 = 60

= \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}, x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

x = \frac{1080 0 ^{\circ} n + 198 0 ^{\circ} - 300}{120}, x = \frac{342 0 ^{\circ} + 1080 0 ^{\circ} n - 300}{60}

作图

流行的例子

tan (x^{2}) + 1 = 0

((1+cos^2(a)))/(sin^2(a))= 5/3

\frac{( 1 + cos ^{2} ( a ) )}{sin ^{2} ( a )} = \frac{5}{3}

d^2+13d+36=(sin^2(x))/2

d^{2} + 13 d + 36 = \frac{sin ^{2} ( x )}{2}

(tan^2(x)-4)/(cos(x)+5)=0

\frac{tan ^{2} ( x ) - 4}{cos ( x ) + 5} = 0

cot^2(x)=sec^2(x)-1

cot^{2} (x) = sec^{2} (x) - 1