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人気のある三角関数 >

(sin(θ))/(140)=(sin(110))/(622)

解

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

解

θ = 0.21311 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21311 \dots + 36 0^{\circ} n

+1

ラジアン

θ = 0.21311 \dots + 2 πn, θ = π - 0.21311 \dots + 2 πn

解答ステップ

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{140} \cdot 10 = \frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

簡素化

\frac{sin ( θ )}{140} \cdot 10 = \frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

簡素化

\frac{sin ( θ )}{140} \cdot 10 : \frac{sin ( θ )}{14}

\frac{sin ( θ )}{140} \cdot 10

分数を乗じる:

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

= \frac{sin ( θ ) \cdot 10}{140}

共通因数を約分する:

10

= \frac{sin ( θ )}{14}

簡素化

\frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10 : \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( 11 0 ^{\circ} )}{622} \cdot 10

分数を乗じる:

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

= \frac{sin ( 11 0 ^{\circ} ) \cdot 10}{622}

共通因数を約分する:

2

= \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

以下で両辺を乗じる:

14

\frac{sin ( θ )}{14} = \frac{5 sin ( 11 0 ^{\circ} )}{311}

以下で両辺を乗じる:

14

\frac{14 sin ( θ )}{14} = \frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

簡素化

\frac{14 sin ( θ )}{14} = \frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

簡素化

\frac{14 sin ( θ )}{14} : sin (θ)

\frac{14 sin ( θ )}{14}

数を割る:

\frac{14}{14} = 1

= sin (θ)

簡素化

\frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311} : \frac{70 sin ( 11 0 ^{\circ} )}{311}

\frac{14 \cdot 5 sin ( 11 0 ^{\circ} )}{311}

数を乗じる:

14 \cdot 5 = 70

= \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

三角関数の逆数プロパティを適用する

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

以下の一般解

sin (θ) = \frac{70 sin ( 11 0 ^{\circ} )}{311}

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

θ = arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n

θ = arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{70 sin ( 11 0 ^{\circ} )}{311}) + 36 0^{\circ} n

10進法形式で解を証明する

θ = 0.21311 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21311 \dots + 36 0^{\circ} n

グラフ

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