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人気のある三角関数 >

(sin(θ))/(20)=(sin(150))/(58.1826)

解

\frac{sin ( θ )}{20} = \frac{sin ( 15 0 ^{\circ} )}{58.1826}

解

θ = 0.17273 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17273 \dots + 36 0^{\circ} n

+1

ラジアン

θ = 0.17273 \dots + 2 πn, θ = π - 0.17273 \dots + 2 πn

解答ステップ

\frac{sin ( θ )}{20} = \frac{sin ( 15 0 ^{\circ} )}{58.1826}

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 0^{\circ})

次の自明恒等式を使用する:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 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{1}{2}

\frac{sin ( θ )}{20} = \frac{\frac{1}{2}}{58.1826}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{20} = \frac{\frac{1}{2}}{58.1826}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{20} \cdot 10 = \frac{\frac{1}{2}}{58.1826} \cdot 10

簡素化

\frac{sin ( θ )}{20} \cdot 10 = \frac{\frac{1}{2}}{58.1826} \cdot 10

簡素化

\frac{sin ( θ )}{20} \cdot 10 : \frac{sin ( θ )}{2}

\frac{sin ( θ )}{20} \cdot 10

分数を乗じる:

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

= \frac{sin ( θ ) \cdot 10}{20}

共通因数を約分する:

10

= \frac{sin ( θ )}{2}

簡素化

\frac{\frac{1}{2}}{58.1826} \cdot 10 : \frac{10}{116.3652}

\frac{\frac{1}{2}}{58.1826} \cdot 10

\frac{\frac{1}{2}}{58.1826} = \frac{1}{116.3652}

\frac{\frac{1}{2}}{58.1826}

分数の規則を適用する:

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

= \frac{1}{2 \cdot 58.1826}

数を乗じる:

2 \cdot 58.1826 = 116.3652

= \frac{1}{116.3652}

= 10 \cdot \frac{1}{116.3652}

分数を乗じる:

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

= \frac{1 \cdot 10}{116.3652}

数を乗じる:

1 \cdot 10 = 10

= \frac{10}{116.3652}

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

以下で両辺を乗じる:

2

\frac{sin ( θ )}{2} = \frac{10}{116.3652}

以下で両辺を乗じる:

2

\frac{2 sin ( θ )}{2} = \frac{10 \cdot 2}{116.3652}

簡素化

\frac{2 sin ( θ )}{2} = \frac{10 \cdot 2}{116.3652}

簡素化

\frac{2 sin ( θ )}{2} : sin (θ)

\frac{2 sin ( θ )}{2}

数を割る:

\frac{2}{2} = 1

= sin (θ)

簡素化

\frac{10 \cdot 2}{116.3652} : \frac{20}{116.3652}

\frac{10 \cdot 2}{116.3652}

数を乗じる:

10 \cdot 2 = 20

= \frac{20}{116.3652}

sin (θ) = \frac{20}{116.3652}

sin (θ) = \frac{20}{116.3652}

sin (θ) = \frac{20}{116.3652}

三角関数の逆数プロパティを適用する

sin (θ) = \frac{20}{116.3652}

以下の一般解

sin (θ) = \frac{20}{116.3652}

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

θ = arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n

θ = arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{20}{116.3652}) + 36 0^{\circ} n

10進法形式で解を証明する

θ = 0.17273 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17273 \dots + 36 0^{\circ} n

グラフ

人気の例

tan (x) = \frac{6}{3}

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