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(x-30)=cos(15)

解答

sin (x - 3 0^{\circ}) = cos (1 5^{\circ})

解答

x = 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}

+1

弧度

x = 1.30899 \dots + \frac{π}{6} + 2 πn, x = π - 1.30899 \dots + \frac{π}{6} + 2 πn

求解步骤

sin (x - 3 0^{\circ}) = cos (1 5^{\circ})

cos (1 5^{\circ}) = \frac{6 + 2}{4}

cos (1 5^{\circ})

使用三角恒等式改写:

cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

cos (1 5^{\circ})

将

cos (1 5^{\circ})

写为

cos (4 5^{\circ} - 3 0^{\circ})

= cos (4 5^{\circ} - 3 0^{\circ})

使用角差恒等式:

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

= cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

= cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

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{2}{2}

使用以下普通恒等式:

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

cos (3 0^{\circ})

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}

使用以下普通恒等式:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

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{2}{2}

使用以下普通恒等式:

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

sin (3 0^{\circ})

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{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

化简

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

\frac{2}{2} \cdot \frac{3}{2}

分式相乘:

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

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

数字相乘:

2 \cdot 2 = 4

= \frac{2 3}{4}

化简

23 : 6

23

使用根式运算法则:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

数字相乘:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

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

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

分式相乘:

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

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

乘以:

2 \cdot 1 = 2

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

数字相乘:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{6}{4} + \frac{2}{4}

使用法则

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

= \frac{6 + 2}{4}

= \frac{6 + 2}{4}

sin (x - 3 0^{\circ}) = \frac{6 + 2}{4}

使用反三角函数性质

sin (x - 3 0^{\circ}) = \frac{6 + 2}{4}

sin (x - 3 0^{\circ}) = \frac{6 + 2}{4}

的通解

sin (x) = a \Rightarrow x = arcsin (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (a) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

解

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n : x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

将

3 0^{\circ}

到右边

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

两边加上

3 0^{\circ}

x - 3 0^{\circ} + 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

化简

x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

解

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

将

3 0^{\circ}

到右边

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

两边加上

3 0^{\circ}

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

化简

x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

以小数形式表示解

x = 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}

作图

流行的例子

tan (x) = 2.8867

3 = cot (q)

sin(t)+cos(2t)=0

sin (t) + cos (2 t) = 0

cos(θ)= 2/3 ,(sin(θ))/2 ,270<θ<360

cos (θ) = \frac{2}{3}, \frac{sin ( θ )}{2}, 27 0^{\circ} < θ < 36 0^{\circ}

cos (9 x) = 0