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人気のある三角関数 >

sin(2x-10)=0.4

解

sin (2 x - 1 0^{\circ}) = 0.4

解

x = 18 0^{\circ} n + \frac{0.41151 \dots}{2} + 5^{\circ}, x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{0.41151 \dots}{2}

+1

ラジアン

x = \frac{0.41151 \dots}{2} + \frac{π}{36} + πn, x = \frac{π}{2} + \frac{π}{36} - \frac{0.41151 \dots}{2} + πn

解答ステップ

sin (2 x - 1 0^{\circ}) = 0.4

三角関数の逆数プロパティを適用する

sin (2 x - 1 0^{\circ}) = 0.4

以下の一般解

sin (2 x - 1 0^{\circ}) = 0.4

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

2 x - 1 0^{\circ} = arcsin (0.4) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsin (0.4) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n

解く

2 x - 1 0^{\circ} = arcsin (0.4) + 36 0^{\circ} n : x = 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

2 x - 1 0^{\circ} = arcsin (0.4) + 36 0^{\circ} n

1 0^{\circ}

を右側に移動します

2 x - 1 0^{\circ} = arcsin (0.4) + 36 0^{\circ} n

両辺に

1 0^{\circ}

を足す

2 x - 1 0^{\circ} + 1 0^{\circ} = arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

簡素化

2 x = arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

2 x = arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

2 x = arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = \frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

\frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

条件のようなグループ

= \frac{36 0 ^{\circ} n}{2} + \frac{arcsin ( 0.4 )}{2} + \frac{1 0 ^{\circ}}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{1 0 ^{\circ}}{2} = 5^{\circ}

\frac{1 0 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{18 \cdot 2}

数を乗じる:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

x = 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

x = 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

x = 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

解く

2 x - 1 0^{\circ} = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n : x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

2 x - 1 0^{\circ} = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n

1 0^{\circ}

を右側に移動します

2 x - 1 0^{\circ} = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n

両辺に

1 0^{\circ}

を足す

2 x - 1 0^{\circ} + 1 0^{\circ} = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

簡素化

2 x = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

2 x = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

2 x = 18 0^{\circ} - arcsin (0.4) + 36 0^{\circ} n + 1 0^{\circ}

以下で両辺を割る

2

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} = 9 0^{\circ} - \frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

9 0^{\circ} - \frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

9 0^{\circ} - \frac{arcsin ( 0.4 )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

条件のようなグループ

= 9 0^{\circ} + \frac{36 0 ^{\circ} n}{2} - \frac{arcsin ( 0.4 )}{2} + \frac{1 0 ^{\circ}}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{1 0 ^{\circ}}{2} = 5^{\circ}

\frac{1 0 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{18 \cdot 2}

数を乗じる:

18 \cdot 2 = 36

= 5^{\circ}

= 9 0^{\circ} + 18 0^{\circ} n - \frac{arcsin ( 0.4 )}{2} + 5^{\circ}

条件のようなグループ

= 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

x = 18 0^{\circ} n + \frac{arcsin ( 0.4 )}{2} + 5^{\circ}, x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{arcsin ( 0.4 )}{2}

10進法形式で解を証明する

x = 18 0^{\circ} n + \frac{0.41151 \dots}{2} + 5^{\circ}, x = 18 0^{\circ} n + 9 0^{\circ} + 5^{\circ} - \frac{0.41151 \dots}{2}

グラフ

人気の例

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