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 >

4cos(x-45)+7=10,0<= x<= 360

解答

4 cos (x - 4 5^{\circ}) + 7 = 10, 0^{\circ} \leq x \leq 36 0^{\circ}

解答

x = \frac{18 0 ^{\circ} + 4 \cdot 0.72273 \dots}{4}, x = \frac{18 0 ^{\circ} - 4 \cdot 0.72273 \dots}{4}

+1

弧度

x = \frac{π + 4 \cdot 0.72273 \dots}{4}, x = \frac{π - 4 \cdot 0.72273 \dots}{4}

求解步骤

4 cos (x - 4 5^{\circ}) + 7 = 10, 0^{\circ} \leq x \leq 36 0^{\circ}

将

7

到右边

4 cos (x - 4 5^{\circ}) + 7 = 10

两边减去

7

4 cos (x - 4 5^{\circ}) + 7 - 7 = 10 - 7

化简

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

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

两边除以

4

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

两边除以

4

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

化简

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

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

使用反三角函数性质

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

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

的通解

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n, x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

解

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n : x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

将

4 5^{\circ}

到右边

x - 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n

两边加上

4 5^{\circ}

x - 4 5^{\circ} + 4 5^{\circ} = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

化简

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

解

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

将

4 5^{\circ}

到右边

x - 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n

两边加上

4 5^{\circ}

x - 4 5^{\circ} + 4 5^{\circ} = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

化简

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

x = arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}, x = 36 0^{\circ} - arccos (\frac{3}{4}) + 36 0^{\circ} n + 4 5^{\circ}

在

0 \leq x \leq 36 0^{\circ}

范围内的解

x = \frac{18 0 ^{\circ} + 4 arccos ( \frac{3}{4} )}{4}, x = \frac{18 0 ^{\circ} - 4 arccos ( \frac{3}{4} )}{4}

以小数形式表示解

x = \frac{18 0 ^{\circ} + 4 \cdot 0.72273 \dots}{4}, x = \frac{18 0 ^{\circ} - 4 \cdot 0.72273 \dots}{4}

作图

流行的例子

6cosh^2(x)+4sinh(x)=7

6 cosh^{2} (x) + 4 sinh (x) = 7

5sqrt(3)tan(x)+3=8sqrt(3)tan(x)

53 tan (x) + 3 = 83 tan (x)

cos^{2} (x) = - 0.5

cos(x)=(1.5)/(4.272)

cos (x) = \frac{1.5}{4.272}

pi/(12)=arcsin(x/2)

\frac{π}{12} = arcsin (\frac{x}{2})