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 >

solvefor θ,cos(θ/2+30)=sin(θ)

解答

求解

θ, cos (\frac{θ}{2} + 3 0^{\circ}) = sin (θ)

解答

θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}, θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

+1

弧度

θ = \frac{2 π}{9} + \frac{12 π}{9} n, θ = \frac{4 π}{3} + \frac{12 π}{3} n

求解步骤

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

使用三角恒等式改写

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

利用以下特性:

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

cos (\frac{θ}{2} + 3 0^{\circ}) = sin (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}))

cos (\frac{θ}{2} + 3 0^{\circ}) = sin (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}))

使用反三角函数性质

cos (\frac{θ}{2} + 3 0^{\circ}) = sin (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}))

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

θ = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n, θ = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n

θ = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n, θ = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n

θ = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n : θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

θ = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n

将

(\frac{θ}{2} + 3 0^{\circ})

para o lado esquerdo

θ = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n

两边加上

(\frac{θ}{2} + 3 0^{\circ})

θ + \frac{θ}{2} + 3 0^{\circ} = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n + \frac{θ}{2} + 3 0^{\circ}

化简

θ + \frac{θ}{2} + 3 0^{\circ} = 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n + \frac{θ}{2} + 3 0^{\circ}

化简

θ + \frac{θ}{2} + 3 0^{\circ} : \frac{9 θ + 18 0 ^{\circ}}{6}

θ + \frac{θ}{2} + 3 0^{\circ}

将项转换为分式:

θ = \frac{θ}{1}

= \frac{θ}{2} + 3 0^{\circ} + \frac{θ}{1}

2, 6, 1

的最小公倍数:

6

2, 6, 1

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

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

1

质因数分解

计算出由至少在以下一个数字中出现的因数组成的数字:

2, 6, 1

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

\frac{θ}{2} :

将分母和分子乘以

3

\frac{θ}{2} = \frac{θ \cdot 3}{2 \cdot 3} = \frac{θ \cdot 3}{6}

对于

\frac{θ}{1} :

将分母和分子乘以

6

\frac{θ}{1} = \frac{θ \cdot 6}{1 \cdot 6} = \frac{θ \cdot 6}{6}

= \frac{θ \cdot 3}{6} + 3 0^{\circ} + \frac{θ \cdot 6}{6}

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{θ \cdot 3 + 18 0 ^{\circ} + θ \cdot 6}{6}

θ \cdot 3 + 18 0^{\circ} + θ \cdot 6 = 9 θ + 18 0^{\circ}

θ \cdot 3 + 18 0^{\circ} + θ \cdot 6

对同类项分组

= 3 θ + 6 θ + 18 0^{\circ}

同类项相加:

3 θ + 6 θ = 9 θ

= 9 θ + 18 0^{\circ}

= \frac{9 θ + 18 0 ^{\circ}}{6}

化简

9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n + \frac{θ}{2} + 3 0^{\circ} : 9 0^{\circ} + 36 0^{\circ} n

9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) + 36 0^{\circ} n + \frac{θ}{2} + 3 0^{\circ}

同类项相加:

- (\frac{θ}{2} + 3 0^{\circ}) + \frac{θ}{2} + 3 0^{\circ} = 0

= 9 0^{\circ} + 36 0^{\circ} n

\frac{9 θ + 18 0 ^{\circ}}{6} = 9 0^{\circ} + 36 0^{\circ} n

\frac{9 θ + 18 0 ^{\circ}}{6} = 9 0^{\circ} + 36 0^{\circ} n

\frac{9 θ + 18 0 ^{\circ}}{6} = 9 0^{\circ} + 36 0^{\circ} n

在两边乘以

6

\frac{9 θ + 18 0 ^{\circ}}{6} = 9 0^{\circ} + 36 0^{\circ} n

在两边乘以

6

\frac{6 ( 9 θ + 18 0 ^{\circ} )}{6} = 6 \cdot 9 0^{\circ} + 6 \cdot 36 0^{\circ} n

化简

\frac{6 ( 9 θ + 18 0 ^{\circ} )}{6} = 6 \cdot 9 0^{\circ} + 6 \cdot 36 0^{\circ} n

化简

\frac{6 ( 9 θ + 18 0 ^{\circ} )}{6} : 9 θ + 18 0^{\circ}

\frac{6 ( 9 θ + 18 0 ^{\circ} )}{6}

数字相除:

\frac{6}{6} = 1

= 9 θ + 18 0^{\circ}

化简

6 \cdot 9 0^{\circ} + 6 \cdot 36 0^{\circ} n : 54 0^{\circ} + 216 0^{\circ} n

6 \cdot 9 0^{\circ} + 6 \cdot 36 0^{\circ} n

6 \cdot 9 0^{\circ} = 54 0^{\circ}

6 \cdot 9 0^{\circ}

分式相乘:

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

= 54 0^{\circ}

数字相除:

\frac{6}{2} = 3

= 54 0^{\circ}

6 \cdot 36 0^{\circ} n = 216 0^{\circ} n

6 \cdot 36 0^{\circ} n

数字相乘:

6 \cdot 2 = 12

= 216 0^{\circ} n

= 54 0^{\circ} + 216 0^{\circ} n

9 θ + 18 0^{\circ} = 54 0^{\circ} + 216 0^{\circ} n

9 θ + 18 0^{\circ} = 54 0^{\circ} + 216 0^{\circ} n

9 θ + 18 0^{\circ} = 54 0^{\circ} + 216 0^{\circ} n

将

18 0^{\circ}

到右边

9 θ + 18 0^{\circ} = 54 0^{\circ} + 216 0^{\circ} n

两边减去

18 0^{\circ}

9 θ + 18 0^{\circ} - 18 0^{\circ} = 54 0^{\circ} + 216 0^{\circ} n - 18 0^{\circ}

化简

9 θ = 36 0^{\circ} + 216 0^{\circ} n

9 θ = 36 0^{\circ} + 216 0^{\circ} n

两边除以

9

9 θ = 36 0^{\circ} + 216 0^{\circ} n

两边除以

9

\frac{9 θ}{9} = 4 0^{\circ} + \frac{216 0 ^{\circ} n}{9}

化简

\frac{9 θ}{9} = 4 0^{\circ} + \frac{216 0 ^{\circ} n}{9}

化简

\frac{9 θ}{9} : θ

\frac{9 θ}{9}

数字相除:

\frac{9}{9} = 1

= θ

化简

4 0^{\circ} + \frac{216 0 ^{\circ} n}{9} : \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

4 0^{\circ} + \frac{216 0 ^{\circ} n}{9}

使用法则

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

= \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}

θ = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n : θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

θ = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n

将

(9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}))

para o lado esquerdo

θ = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n

两边加上

(9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}))

θ + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})

化简

θ + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) = 18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})

化简

θ + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) : \frac{3 θ + 36 0 ^{\circ}}{6}

θ + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})

- (\frac{θ}{2} + 3 0^{\circ}) : - \frac{θ}{2} - 3 0^{\circ}

- (\frac{θ}{2} + 3 0^{\circ})

打开括号

= - (\frac{θ}{2}) - (3 0^{\circ})

使用加减运算法则

+ (- a) = - a

= - \frac{θ}{2} - 3 0^{\circ}

= θ + 9 0^{\circ} - \frac{θ}{2} - 3 0^{\circ}

化简

θ + 9 0^{\circ} - \frac{θ}{2} - 3 0^{\circ} : \frac{3 θ + 36 0 ^{\circ}}{6}

θ + 9 0^{\circ} - \frac{θ}{2} - 3 0^{\circ}

对同类项分组

= θ - \frac{θ}{2} + 9 0^{\circ} - 3 0^{\circ}

合并分式

- \frac{θ}{2} + 9 0^{\circ} : \frac{- θ + 18 0 ^{\circ}}{2}

使用法则

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

= \frac{- θ + 18 0 ^{\circ}}{2}

= θ + \frac{- θ + 18 0 ^{\circ}}{2} - 3 0^{\circ}

将项转换为分式:

θ = \frac{θ}{1}

= \frac{- θ + 18 0 ^{\circ}}{2} - 3 0^{\circ} + \frac{θ}{1}

2, 6, 1

的最小公倍数:

6

2, 6, 1

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

6

质因数分解:

2 \cdot 3

6

6

除以

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

都是质数，因此无法进一步因数分解

= 2 \cdot 3

1

质因数分解

计算出由至少在以下一个数字中出现的因数组成的数字:

2, 6, 1

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

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

6

对于

\frac{- θ + 18 0 ^{\circ}}{2} :

将分母和分子乘以

3

\frac{- θ + 18 0 ^{\circ}}{2} = \frac{( - θ + 18 0 ^{\circ} ) \cdot 3}{2 \cdot 3} = \frac{( - θ + 18 0 ^{\circ} ) \cdot 3}{6}

对于

\frac{θ}{1} :

将分母和分子乘以

6

\frac{θ}{1} = \frac{θ \cdot 6}{1 \cdot 6} = \frac{θ \cdot 6}{6}

= \frac{( - θ + 18 0 ^{\circ} ) \cdot 3}{6} - 3 0^{\circ} + \frac{θ \cdot 6}{6}

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{( - θ + 18 0 ^{\circ} ) \cdot 3 - 18 0 ^{\circ} + θ \cdot 6}{6}

乘开

(- θ + 18 0^{\circ}) \cdot 3 - 18 0^{\circ} + θ \cdot 6 : 3 θ + 36 0^{\circ}

(- θ + 18 0^{\circ}) \cdot 3 - 18 0^{\circ} + θ \cdot 6

= 3 (- θ + 18 0^{\circ}) - 18 0^{\circ} + 6 θ

乘开

3 (- θ + 18 0^{\circ}) : - 3 θ + 54 0^{\circ}

3 (- θ + 18 0^{\circ})

使用分配律:

a (b + c) = ab + a c

a = 3, b = - θ, c = 18 0^{\circ}

= 3 (- θ) + 54 0^{\circ}

使用加减运算法则

+ (- a) = - a

= - 3 θ + 54 0^{\circ}

= - 3 θ + 54 0^{\circ} - 18 0^{\circ} + θ \cdot 6

化简

- 3 θ + 54 0^{\circ} - 18 0^{\circ} + θ \cdot 6 : 3 θ + 36 0^{\circ}

- 3 θ + 54 0^{\circ} - 18 0^{\circ} + θ \cdot 6

对同类项分组

= - 3 θ + 6 θ + 54 0^{\circ} - 18 0^{\circ}

同类项相加:

- 3 θ + 6 θ = 3 θ

= 3 θ + 54 0^{\circ} - 18 0^{\circ}

同类项相加:

54 0^{\circ} - 18 0^{\circ} = 36 0^{\circ}

= 3 θ + 36 0^{\circ}

= 3 θ + 36 0^{\circ}

= \frac{3 θ + 36 0 ^{\circ}}{6}

= \frac{3 θ + 36 0 ^{\circ}}{6}

化简

18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) : 18 0^{\circ} + 36 0^{\circ} n

18 0^{\circ} - (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 36 0^{\circ} n + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})

同类项相加:

- (9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ})) + 9 0^{\circ} - (\frac{θ}{2} + 3 0^{\circ}) = 0

= 18 0^{\circ} + 36 0^{\circ} n

\frac{3 θ + 36 0 ^{\circ}}{6} = 18 0^{\circ} + 36 0^{\circ} n

\frac{3 θ + 36 0 ^{\circ}}{6} = 18 0^{\circ} + 36 0^{\circ} n

\frac{3 θ + 36 0 ^{\circ}}{6} = 18 0^{\circ} + 36 0^{\circ} n

在两边乘以

6

\frac{3 θ + 36 0 ^{\circ}}{6} = 18 0^{\circ} + 36 0^{\circ} n

在两边乘以

6

\frac{6 ( 3 θ + 36 0 ^{\circ} )}{6} = 108 0^{\circ} + 6 \cdot 36 0^{\circ} n

化简

3 θ + 36 0^{\circ} = 108 0^{\circ} + 216 0^{\circ} n

3 θ + 36 0^{\circ} = 108 0^{\circ} + 216 0^{\circ} n

将

36 0^{\circ}

到右边

3 θ + 36 0^{\circ} = 108 0^{\circ} + 216 0^{\circ} n

两边减去

36 0^{\circ}

3 θ + 36 0^{\circ} - 36 0^{\circ} = 108 0^{\circ} + 216 0^{\circ} n - 36 0^{\circ}

化简

3 θ = 72 0^{\circ} + 216 0^{\circ} n

3 θ = 72 0^{\circ} + 216 0^{\circ} n

两边除以

3

3 θ = 72 0^{\circ} + 216 0^{\circ} n

两边除以

3

\frac{3 θ}{3} = 24 0^{\circ} + \frac{216 0 ^{\circ} n}{3}

化简

\frac{3 θ}{3} = 24 0^{\circ} + \frac{216 0 ^{\circ} n}{3}

化简

\frac{3 θ}{3} : θ

\frac{3 θ}{3}

数字相除:

\frac{3}{3} = 1

= θ

化简

24 0^{\circ} + \frac{216 0 ^{\circ} n}{3} : \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

24 0^{\circ} + \frac{216 0 ^{\circ} n}{3}

使用法则

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

= \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}, θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

θ = \frac{36 0 ^{\circ} + 216 0 ^{\circ} n}{9}, θ = \frac{72 0 ^{\circ} + 216 0 ^{\circ} n}{3}

作图

流行的例子

5sin^2(θ)=1+3sin^2(θ)

5 sin^{2} (θ) = 1 + 3 sin^{2} (θ)

5sin(2θ)-8sin(θ)=0

5 sin (2 θ) - 8 sin (θ) = 0

tan(θ)=(5sqrt(3))/5

tan (θ) = \frac{5 3}{5}

solvefor f,r= 8/(sec(f^0))

so l v e f or f, r = \frac{8}{sec ( f ^{0} )}

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

2 sin (x) - 2 = 0, 0 \leq x \leq 2 π