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人気のある三角関数 >

(sin(50))/(10)=(sin(q))/(12)

解

\frac{sin ( 5 0 ^{\circ} )}{10} = \frac{sin ( q )}{12}

解

q = 1.16617 \dots + 36 0^{\circ} n, q = 18 0^{\circ} - 1.16617 \dots + 36 0^{\circ} n

+1

ラジアン

q = 1.16617 \dots + 2 πn, q = π - 1.16617 \dots + 2 πn

解答ステップ

\frac{sin ( 5 0 ^{\circ} )}{10} = \frac{sin ( q )}{12}

辺を交換する

\frac{sin ( q )}{12} = \frac{sin ( 5 0 ^{\circ} )}{10}

以下で両辺を乗じる:

10

\frac{sin ( q )}{12} = \frac{sin ( 5 0 ^{\circ} )}{10}

以下で両辺を乗じる:

10

\frac{sin ( q )}{12} \cdot 10 = \frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10

簡素化

\frac{sin ( q )}{12} \cdot 10 = \frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10

簡素化

\frac{sin ( q )}{12} \cdot 10 : \frac{5 sin ( q )}{6}

\frac{sin ( q )}{12} \cdot 10

分数を乗じる:

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

= \frac{sin ( q ) \cdot 10}{12}

共通因数を約分する:

2

= \frac{5 sin ( q )}{6}

簡素化

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

\frac{sin ( 5 0 ^{\circ} )}{10} \cdot 10

分数を乗じる:

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

= \frac{sin ( 5 0 ^{\circ} ) \cdot 10}{10}

共通因数を約分する:

10

= sin (5 0^{\circ})

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

以下で両辺を乗じる:

6

\frac{5 sin ( q )}{6} = sin (5 0^{\circ})

以下で両辺を乗じる:

6

\frac{6 \cdot 5 sin ( q )}{6} = 6 sin (5 0^{\circ})

簡素化

5 sin (q) = 6 sin (5 0^{\circ})

5 sin (q) = 6 sin (5 0^{\circ})

以下で両辺を割る

5

5 sin (q) = 6 sin (5 0^{\circ})

以下で両辺を割る

5

\frac{5 sin ( q )}{5} = \frac{6 sin ( 5 0 ^{\circ} )}{5}

簡素化

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

三角関数の逆数プロパティを適用する

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

以下の一般解

sin (q) = \frac{6 sin ( 5 0 ^{\circ} )}{5}

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

q = arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n, q = 18 0^{\circ} - arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n

q = arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n, q = 18 0^{\circ} - arcsin (\frac{6 sin ( 5 0 ^{\circ} )}{5}) + 36 0^{\circ} n

10進法形式で解を証明する

q = 1.16617 \dots + 36 0^{\circ} n, q = 18 0^{\circ} - 1.16617 \dots + 36 0^{\circ} n

グラフ

人気の例

271.63=(3sqrt(3)*169.7)/pi cos(α)

271.63 = \frac{3 3 \cdot 169.7}{π} cos (α)

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