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受欢迎的三角函数 >

cos(5x+40)= 3/5

解答

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

解答

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

+1

弧度

x = - \frac{2 π}{45} + \frac{0.92729 \dots}{5} + \frac{2 π}{5} n, x = \frac{2 π}{5} - \frac{2 π}{45} - \frac{0.92729 \dots}{5} + \frac{2 π}{5} n

求解步骤

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

使用反三角函数性质

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

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

的通解

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

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

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

解

5 x + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n : x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

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

将

4 0^{\circ}

到右边

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

两边减去

4 0^{\circ}

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

化简

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

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

两边除以

5

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

两边除以

5

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

化简

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

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

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

对同类项分组

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

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

使用分式法则:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

数字相乘:

9 \cdot 5 = 45

= 8^{\circ}

= \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

解

5 x + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n : x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

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

将

4 0^{\circ}

到右边

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

两边减去

4 0^{\circ}

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

化简

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

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

两边除以

5

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

两边除以

5

\frac{5 x}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

化简

\frac{5 x}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

化简

\frac{5 x}{5} : x

\frac{5 x}{5}

数字相除:

\frac{5}{5} = 1

= x

化简

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

对同类项分组

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} - \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

使用分式法则:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

数字相乘:

9 \cdot 5 = 45

= 8^{\circ}

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - 8^{\circ} - \frac{arccos ( \frac{3}{5} )}{5}

对同类项分组

= 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}, x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

以小数形式表示解

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

作图

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