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人気のある三角関数 >

sin(90-a)= 1/(1.63)

解

sin (9 0^{\circ} - a) = \frac{1}{1.63}

解

a = - 36 0^{\circ} n + 9 0^{\circ} - 0.66048 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.66048 \dots

+1

ラジアン

a = \frac{π}{2} - 0.66048 \dots - 2 πn, a = - π + \frac{π}{2} + 0.66048 \dots - 2 πn

解答ステップ

sin (9 0^{\circ} - a) = \frac{1}{1.63}

三角関数の逆数プロパティを適用する

sin (9 0^{\circ} - a) = \frac{1}{1.63}

以下の一般解

sin (9 0^{\circ} - a) = \frac{1}{1.63}

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

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n, 9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n, 9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

解く

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n : a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

9 0^{\circ}

を右側に移動します

9 0^{\circ} - a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

両辺から

9 0^{\circ}

を引く

9 0^{\circ} - a - 9 0^{\circ} = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

簡素化

- a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

- a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

以下で両辺を割る

- 1

- a = arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

以下で両辺を割る

- 1

\frac{- a}{- 1} = \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

簡素化

\frac{- a}{- 1} = \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

簡素化

\frac{- a}{- 1} : a

\frac{- a}{- 1}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{a}{1}

規則を適用

\frac{a}{1} = a

= a

簡素化

\frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

\frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

条件のようなグループ

= \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} + \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

規則を適用

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} + \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{9 0 ^{\circ}}{1}

分数の規則を適用する:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{arcsin ( \frac{1}{1.63} )}{- 1} = - arcsin (\frac{1}{1.63})

\frac{arcsin ( \frac{1}{1.63} )}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{1}{1.63} )}{1}

分数の規則を適用する:

\frac{a}{1} = a

\frac{arcsin ( \frac{1}{1.63} )}{1} = arcsin (\frac{1}{1.63})

= - arcsin (\frac{1}{1.63})

= - 36 0^{\circ} n - (- 9 0^{\circ}) - arcsin (\frac{1}{1.63})

規則を適用

- (- a) = a

= - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63})

解く

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n : a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

9 0^{\circ}

を右側に移動します

9 0^{\circ} - a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n

両辺から

9 0^{\circ}

を引く

9 0^{\circ} - a - 9 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

簡素化

- a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

- a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

以下で両辺を割る

- 1

- a = 18 0^{\circ} - arcsin (\frac{1}{1.63}) + 36 0^{\circ} n - 9 0^{\circ}

以下で両辺を割る

- 1

\frac{- a}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

簡素化

\frac{- a}{- 1} = \frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

簡素化

\frac{- a}{- 1} : a

\frac{- a}{- 1}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{a}{1}

規則を適用

\frac{a}{1} = a

= a

簡素化

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} : - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

\frac{18 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1}

条件のようなグループ

= \frac{18 0 ^{\circ}}{- 1} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{18 0 ^{\circ}}{- 1} = - 18 0^{\circ}

\frac{18 0 ^{\circ}}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - 18 0^{\circ}

規則を適用

\frac{a}{1} = a

= - 18 0^{\circ}

= - 18 0^{\circ} + \frac{36 0 ^{\circ} n}{- 1} - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{36 0 ^{\circ} n}{- 1} = - 36 0^{\circ} n

\frac{36 0 ^{\circ} n}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{36 0 ^{\circ} n}{1}

規則を適用

\frac{a}{1} = a

= - 36 0^{\circ} n

= - 18 0^{\circ} - 36 0^{\circ} n - \frac{9 0 ^{\circ}}{- 1} - \frac{arcsin ( \frac{1}{1.63} )}{- 1}

\frac{9 0 ^{\circ}}{- 1} = - 9 0^{\circ}

\frac{9 0 ^{\circ}}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{9 0 ^{\circ}}{1}

分数の規則を適用する:

\frac{a}{1} = a

\frac{9 0 ^{\circ}}{1} = 9 0^{\circ}

= - 9 0^{\circ}

\frac{arcsin ( \frac{1}{1.63} )}{- 1} = - arcsin (\frac{1}{1.63})

\frac{arcsin ( \frac{1}{1.63} )}{- 1}

分数の規則を適用する:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arcsin ( \frac{1}{1.63} )}{1}

分数の規則を適用する:

\frac{a}{1} = a

\frac{arcsin ( \frac{1}{1.63} )}{1} = arcsin (\frac{1}{1.63})

= - arcsin (\frac{1}{1.63})

= - 18 0^{\circ} - 36 0^{\circ} n - (- 9 0^{\circ}) - (- arcsin (\frac{1}{1.63}))

規則を適用

- (- a) = a

= - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

a = - 36 0^{\circ} n + 9 0^{\circ} - arcsin (\frac{1}{1.63}), a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + arcsin (\frac{1}{1.63})

10進法形式で解を証明する

a = - 36 0^{\circ} n + 9 0^{\circ} - 0.66048 \dots, a = - 18 0^{\circ} - 36 0^{\circ} n + 9 0^{\circ} + 0.66048 \dots

グラフ

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