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人気のある三角関数 >

sin(x-30)=cos(15)

解

sin (x - 3 0^{\circ}) = cos (1 5^{\circ})

解

x = 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}

+1

ラジアン

x = 1.30899 \dots + \frac{π}{6} + 2 πn, x = π - 1.30899 \dots + \frac{π}{6} + 2 πn

解答ステップ

sin (x - 3 0^{\circ}) = cos (1 5^{\circ})

cos (1 5^{\circ}) = \frac{6 + 2}{4}

cos (1 5^{\circ})

三角関数の公式を使用して書き換える:

cos (4 5^{\circ}) cos (3 0^{\circ}) + sin (4 5^{\circ}) sin (3 0^{\circ})

cos (1 5^{\circ})

cos (1 5^{\circ})

を以下として書く:

cos (4 5^{\circ} - 3 0^{\circ})

= cos (4 5^{\circ} - 3 0^{\circ})

角の差の公式を使用する:

cos (s - t) = cos (s) cos (t) + sin (s) sin (t)

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

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

次の自明恒等式を使用する:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

次の自明恒等式を使用する:

cos (3 0^{\circ}) = \frac{3}{2}

cos (3 0^{\circ})

cos (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

次の自明恒等式を使用する:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

sin (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

次の自明恒等式を使用する:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

簡素化

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2} : \frac{6 + 2}{4}

\frac{2}{2} \cdot \frac{3}{2} + \frac{2}{2} \cdot \frac{1}{2}

\frac{2}{2} \cdot \frac{3}{2} = \frac{6}{4}

\frac{2}{2} \cdot \frac{3}{2}

分数を乗じる:

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

= \frac{2 3}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{2 3}{4}

簡素化

23 : 6

23

累乗根の規則を適用する:

a b = a \cdot b

23 = 2 \cdot 3

= 2 \cdot 3

数を乗じる:

2 \cdot 3 = 6

= 6

= \frac{6}{4}

\frac{2}{2} \cdot \frac{1}{2} = \frac{2}{4}

\frac{2}{2} \cdot \frac{1}{2}

分数を乗じる:

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

= \frac{2 \cdot 1}{2 \cdot 2}

乗算:

2 \cdot 1 = 2

= \frac{2}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{2}{4}

= \frac{6}{4} + \frac{2}{4}

規則を適用

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

= \frac{6 + 2}{4}

= \frac{6 + 2}{4}

sin (x - 3 0^{\circ}) = \frac{6 + 2}{4}

三角関数の逆数プロパティを適用する

sin (x - 3 0^{\circ}) = \frac{6 + 2}{4}

以下の一般解

sin (x - 3 0^{\circ}) = \frac{6 + 2}{4}

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

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n, x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

解く

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n : x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

3 0^{\circ}

を右側に移動します

x - 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

両辺に

3 0^{\circ}

を足す

x - 3 0^{\circ} + 3 0^{\circ} = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

簡素化

x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

解く

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

3 0^{\circ}

を右側に移動します

x - 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n

両辺に

3 0^{\circ}

を足す

x - 3 0^{\circ} + 3 0^{\circ} = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

簡素化

x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

x = arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - arcsin (\frac{6 + 2}{4}) + 36 0^{\circ} n + 3 0^{\circ}

10進法形式で解を証明する

x = 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}, x = 18 0^{\circ} - 1.30899 \dots + 36 0^{\circ} n + 3 0^{\circ}

グラフ

人気の例

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