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^2(a)=-((5sqrt(11)))/((18))

解答

sin^{2} (a) = - \frac{( 5 11 )}{( 18 )}

解答

a \in R 无解

求解步骤

sin^{2} (a) = - \frac{( 5 11 )}{( 18 )}

用替代法求解

sin^{2} (a) = - \frac{5 11}{18}

令

: sin (a) = u

u^{2} = - \frac{5 11}{18}

u^{2} = - \frac{5 11}{18} : u = i \frac{4 11 10}{6}, u = - i \frac{4 11 10}{6}

u^{2} = - \frac{5 11}{18}

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = - \frac{5 11}{18}, u = - - \frac{5 11}{18}

化简

- \frac{5 11}{18} : i \frac{4 11 10}{6}

- \frac{5 11}{18}

使用根式运算法则:

- a = - 1 a

- \frac{5 11}{18} = - 1 \frac{5 11}{18}

= - 1 \frac{5 11}{18}

使用虚数运算法则:

- 1 = i

= i \frac{5 11}{18}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

\frac{5 11}{18} = \frac{5 11}{18}

= i \frac{5 11}{18}

18 = 32

18

18

质因数分解:

2 \cdot 3^{2}

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

= 2 \cdot 3^{2}

= 3^{2} \cdot 2

使用根式运算法则:

n ab = n a n b

= 2 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 32

= i \frac{5 11}{3 2}

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

511 = 511

= i \frac{5 11}{3 2}

11 : 411

使用根式运算法则:

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

= (1 1^{\frac{1}{2}})^{\frac{1}{2}}

使用指数法则:

(a^{b})^{c} = a^{b c}

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

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

分式相乘:

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

= \frac{1 \cdot 1}{2 \cdot 2}

数字相乘:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

= 1 1^{\frac{1}{4}}

a^{\frac{1}{n}} = n a

= 411

= i \frac{5 4 11}{3 2}

\frac{5 4 11}{3 2} = \frac{10 4 11}{6}

\frac{5 4 11}{3 2}

乘以共轭根式

\frac{2}{2}

= \frac{5 4 11 2}{3 2 2}

54112 = 10411

54112

使用根式运算法则:

a b = a \cdot b

52 = 5 \cdot 2

= 411 5 \cdot 2

数字相乘:

5 \cdot 2 = 10

= 10411

322 = 6

322

使用根式运算法则:

a a = a

22 = 2

= 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

= \frac{10 4 11}{6}

= i \frac{10 4 11}{6}

将

i \frac{10 4 11}{6}

改写成标准复数形式:

\frac{10 4 11}{6} i

i \frac{10 4 11}{6}

\frac{10 4 11}{6} = \frac{5 4 11}{3 2}

\frac{10 4 11}{6}

分解

10 : 25

因式分解

10 = 2 \cdot 5

= 2 \cdot 5

使用根式运算法则:

n ab = n a n b

= 25

分解

6 : 2 \cdot 3

因式分解

6 = 2 \cdot 3

= \frac{2 5 4 11}{2 \cdot 3}

消掉

\frac{2 5 4 11}{2 \cdot 3} : \frac{5 4 11}{2 \cdot 3}

\frac{2 5 4 11}{2 \cdot 3}

使用根式运算法则:

n a = a^{\frac{1}{n}}

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

= \frac{2 ^{\frac{1}{2}} 5 4 11}{2 \cdot 3}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{5 4 11}{3 \cdot 2 ^{- \frac{1}{2} + 1}}

数字相减:

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

= \frac{5 4 11}{3 \cdot 2 ^{\frac{1}{2}}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

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

= \frac{5 4 11}{3 2}

= \frac{5 4 11}{2 \cdot 3}

= i \frac{5 4 11}{3 2}

分式相乘:

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

= \frac{5 4 11 i}{2 \cdot 3}

\frac{5 4 11}{3 2} = \frac{10 4 11}{6}

\frac{5 4 11}{3 2}

乘以共轭根式

\frac{2}{2}

= \frac{5 4 11 2}{3 2 2}

54112 = 10411

54112

使用根式运算法则:

a b = a \cdot b

52 = 5 \cdot 2

= 411 5 \cdot 2

数字相乘:

5 \cdot 2 = 10

= 10411

322 = 6

322

使用根式运算法则:

a a = a

22 = 2

= 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

= \frac{10 4 11}{6}

= \frac{10 4 11}{6} i

= \frac{10 4 11}{6} i

化简

- - \frac{5 11}{18} : - i \frac{4 11 10}{6}

- - \frac{5 11}{18}

化简

- \frac{5 11}{18} : i \frac{5 4 11}{3 2}

- \frac{5 11}{18}

使用根式运算法则:

- a = - 1 a

- \frac{5 11}{18} = - 1 \frac{5 11}{18}

= - 1 \frac{5 11}{18}

使用虚数运算法则:

- 1 = i

= i \frac{5 11}{18}

使用根式运算法则:

n \frac{a}{b} = \frac{n a}{n b},

假定

a \geq 0, b \geq 0

\frac{5 11}{18} = \frac{5 11}{18}

= i \frac{5 11}{18}

18 = 32

18

18

质因数分解:

2 \cdot 3^{2}

18

18

除以

218 = 9 \cdot 2

= 2 \cdot 9

9

除以

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3 \cdot 3

= 2 \cdot 3^{2}

= 3^{2} \cdot 2

使用根式运算法则:

n ab = n a n b

= 2 3^{2}

使用根式运算法则:

n a^{n} = a

3^{2} = 3

= 32

= i \frac{5 11}{3 2}

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

511 = 511

= i \frac{5 11}{3 2}

11 : 411

使用根式运算法则:

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

= (1 1^{\frac{1}{2}})^{\frac{1}{2}}

使用指数法则:

(a^{b})^{c} = a^{b c}

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

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

\frac{1}{2} \cdot \frac{1}{2}

分式相乘:

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

= \frac{1 \cdot 1}{2 \cdot 2}

数字相乘:

1 \cdot 1 = 1

= \frac{1}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{1}{4}

= 1 1^{\frac{1}{4}}

a^{\frac{1}{n}} = n a

= 411

= i \frac{5 4 11}{3 2}

= - i \frac{5 4 11}{3 2}

\frac{5 4 11}{3 2} = \frac{10 4 11}{6}

\frac{5 4 11}{3 2}

乘以共轭根式

\frac{2}{2}

= \frac{5 4 11 2}{3 2 2}

54112 = 10411

54112

使用根式运算法则:

a b = a \cdot b

52 = 5 \cdot 2

= 411 5 \cdot 2

数字相乘:

5 \cdot 2 = 10

= 10411

322 = 6

322

使用根式运算法则:

a a = a

22 = 2

= 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

= \frac{10 4 11}{6}

= - i \frac{10 4 11}{6}

将

- i \frac{10 4 11}{6}

改写成标准复数形式:

- \frac{10 4 11}{6} i

- i \frac{10 4 11}{6}

\frac{10 4 11}{6} = \frac{5 4 11}{3 2}

\frac{10 4 11}{6}

分解

10 : 25

因式分解

10 = 2 \cdot 5

= 2 \cdot 5

使用根式运算法则:

n ab = n a n b

= 25

分解

6 : 2 \cdot 3

因式分解

6 = 2 \cdot 3

= \frac{2 5 4 11}{2 \cdot 3}

消掉

\frac{2 5 4 11}{2 \cdot 3} : \frac{5 4 11}{2 \cdot 3}

\frac{2 5 4 11}{2 \cdot 3}

使用根式运算法则:

n a = a^{\frac{1}{n}}

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

= \frac{2 ^{\frac{1}{2}} 5 4 11}{2 \cdot 3}

使用指数法则:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{5 4 11}{3 \cdot 2 ^{- \frac{1}{2} + 1}}

数字相减:

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

= \frac{5 4 11}{3 \cdot 2 ^{\frac{1}{2}}}

使用根式运算法则:

a^{\frac{1}{n}} = n a

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

= \frac{5 4 11}{3 2}

= \frac{5 4 11}{2 \cdot 3}

= - i \frac{5 4 11}{3 2}

分式相乘:

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

= - \frac{5 4 11 i}{2 \cdot 3}

- \frac{5 4 11}{3 2} = - \frac{10 4 11}{6}

- \frac{5 4 11}{3 2}

乘以共轭根式

\frac{2}{2}

= - \frac{5 4 11 2}{3 2 2}

54112 = 10411

54112

使用根式运算法则:

a b = a \cdot b

52 = 5 \cdot 2

= 411 5 \cdot 2

数字相乘:

5 \cdot 2 = 10

= 10411

322 = 6

322

使用根式运算法则:

a a = a

22 = 2

= 3 \cdot 2

数字相乘:

3 \cdot 2 = 6

= 6

= - \frac{10 4 11}{6}

= - \frac{10 4 11}{6} i

= - \frac{10 4 11}{6} i

u = i \frac{4 11 10}{6}, u = - i \frac{4 11 10}{6}

u = sin (a)

代回

sin (a) = i \frac{4 11 10}{6}, sin (a) = - i \frac{4 11 10}{6}

sin (a) = i \frac{4 11 10}{6}, sin (a) = - i \frac{4 11 10}{6}

sin (a) = i \frac{4 11 10}{6} :

无解

sin (a) = i \frac{4 11 10}{6}

无解

sin (a) = - i \frac{4 11 10}{6} :

无解

sin (a) = - i \frac{4 11 10}{6}

无解

合并所有解

a \in R 无解

作图

流行的例子

3.87sin((2pi(t+101.75))/(365))+11.7=14

3.87 sin (\frac{2 π ( t + 101.75 )}{365}) + 11.7 = 14

2sin(2x)=sqrt(3),0<= x<= 2pi

2 sin (2 x) = 3, 0 \leq x \leq 2 π

cosh(2x)+sinh^2(x)-13sinh(x)=-3

cosh (2 x) + sinh^{2} (x) - 13 sinh (x) = - 3

sin (3 x - \frac{π}{4}) = 1

(1-tan^2(A))/(1+tan^2(A))=1

\frac{1 - tan ^{2} ( A )}{1 + tan ^{2} ( A )} = 1