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人気のある三角関数 >

5sin(2x-pi/2)=0.5

解

5 sin (2 x - \frac{π}{2}) = 0.5

解

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

+1

度

x = 47.86958 \dots^{\circ} + 18 0^{\circ} n, x = 132.13041 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

5 sin (2 x - \frac{π}{2}) = 0.5

以下で両辺を割る

5

5 sin (2 x - \frac{π}{2}) = 0.5

以下で両辺を割る

5

\frac{5 sin ( 2 x - \frac{π}{2} )}{5} = \frac{0.5}{5}

簡素化

sin (2 x - \frac{π}{2}) = 0.1

sin (2 x - \frac{π}{2}) = 0.1

三角関数の逆数プロパティを適用する

sin (2 x - \frac{π}{2}) = 0.1

以下の一般解

sin (2 x - \frac{π}{2}) = 0.1

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn, 2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn, 2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

解く

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn : x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn

\frac{π}{2}

を右側に移動します

2 x - \frac{π}{2} = arcsin (0.1) + 2 πn

両辺に

\frac{π}{2}

を足す

2 x - \frac{π}{2} + \frac{π}{2} = arcsin (0.1) + 2 πn + \frac{π}{2}

簡素化

2 x = arcsin (0.1) + 2 πn + \frac{π}{2}

2 x = arcsin (0.1) + 2 πn + \frac{π}{2}

以下で両辺を割る

2

2 x = arcsin (0.1) + 2 πn + \frac{π}{2}

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

簡素化

\frac{2 x}{2} = \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{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 ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} : πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

\frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

条件のようなグループ

= \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} + \frac{arcsin ( 0.1 )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

分数の規則を適用する:

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

= \frac{π}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{π}{4}

= πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}

解く

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn : x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

\frac{π}{2}

を右側に移動します

2 x - \frac{π}{2} = π - arcsin (0.1) + 2 πn

両辺に

\frac{π}{2}

を足す

2 x - \frac{π}{2} + \frac{π}{2} = π - arcsin (0.1) + 2 πn + \frac{π}{2}

簡素化

2 x = π - arcsin (0.1) + 2 πn + \frac{π}{2}

2 x = π - arcsin (0.1) + 2 πn + \frac{π}{2}

以下で両辺を割る

2

2 x = π - arcsin (0.1) + 2 πn + \frac{π}{2}

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

簡素化

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{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{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} : πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

\frac{π}{2} - \frac{arcsin ( 0.1 )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2}

条件のようなグループ

= \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{2}}{2} - \frac{arcsin ( 0.1 )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{2}}{2} = \frac{π}{4}

\frac{\frac{π}{2}}{2}

分数の規則を適用する:

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

= \frac{π}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{π}{4}

= \frac{π}{2} + πn + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

条件のようなグループ

= πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

x = πn + \frac{π}{4} + \frac{arcsin ( 0.1 )}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{arcsin ( 0.1 )}{2}

10進法形式で解を証明する

x = πn + \frac{π}{4} + \frac{0.10016 \dots}{2}, x = πn + \frac{π}{2} + \frac{π}{4} - \frac{0.10016 \dots}{2}

グラフ

人気の例

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