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人気のある三角関数 >

(sin(x))/5 =(sin(125))/(20)

解

\frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

解

x = 0.20624 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.20624 \dots + 36 0^{\circ} n

+1

ラジアン

x = 0.20624 \dots + 2 πn, x = π - 0.20624 \dots + 2 πn

解答ステップ

\frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

以下で両辺を乗じる:

10

\frac{sin ( x )}{5} = \frac{sin ( 12 5 ^{\circ} )}{20}

以下で両辺を乗じる:

10

\frac{sin ( x )}{5} \cdot 10 = \frac{sin ( 12 5 ^{\circ} )}{20} \cdot 10

簡素化

\frac{sin ( x )}{5} \cdot 10 = \frac{sin ( 12 5 ^{\circ} )}{20} \cdot 10

簡素化

\frac{sin ( x )}{5} \cdot 10 : 2 sin (x)

\frac{sin ( x )}{5} \cdot 10

分数を乗じる:

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

= \frac{sin ( x ) \cdot 10}{5}

数を割る:

\frac{10}{5} = 2

= 2 sin (x)

簡素化

\frac{sin ( 12 5 ^{\circ} )}{20} \cdot 10 : \frac{sin ( 12 5 ^{\circ} )}{2}

\frac{sin ( 12 5 ^{\circ} )}{20} \cdot 10

分数を乗じる:

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

= \frac{sin ( 12 5 ^{\circ} ) \cdot 10}{20}

共通因数を約分する:

10

= \frac{sin ( 12 5 ^{\circ} )}{2}

2 sin (x) = \frac{sin ( 12 5 ^{\circ} )}{2}

2 sin (x) = \frac{sin ( 12 5 ^{\circ} )}{2}

2 sin (x) = \frac{sin ( 12 5 ^{\circ} )}{2}

以下で両辺を割る

2

2 sin (x) = \frac{sin ( 12 5 ^{\circ} )}{2}

以下で両辺を割る

2

\frac{2 sin ( x )}{2} = \frac{\frac{s i n ( 12 5 ^{\circ} )}{2}}{2}

簡素化

\frac{2 sin ( x )}{2} = \frac{\frac{s i n ( 12 5 ^{\circ} )}{2}}{2}

簡素化

\frac{2 sin ( x )}{2} : sin (x)

\frac{2 sin ( x )}{2}

数を割る:

\frac{2}{2} = 1

= sin (x)

簡素化

\frac{\frac{s i n ( 12 5 ^{\circ} )}{2}}{2} : \frac{sin ( 12 5 ^{\circ} )}{4}

\frac{\frac{s i n ( 12 5 ^{\circ} )}{2}}{2}

分数の規則を適用する:

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

= \frac{sin ( 12 5 ^{\circ} )}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{sin ( 12 5 ^{\circ} )}{4}

sin (x) = \frac{sin ( 12 5 ^{\circ} )}{4}

sin (x) = \frac{sin ( 12 5 ^{\circ} )}{4}

sin (x) = \frac{sin ( 12 5 ^{\circ} )}{4}

三角関数の逆数プロパティを適用する

sin (x) = \frac{sin ( 12 5 ^{\circ} )}{4}

以下の一般解

sin (x) = \frac{sin ( 12 5 ^{\circ} )}{4}

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

x = arcsin (\frac{sin ( 12 5 ^{\circ} )}{4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 12 5 ^{\circ} )}{4}) + 36 0^{\circ} n

x = arcsin (\frac{sin ( 12 5 ^{\circ} )}{4}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{sin ( 12 5 ^{\circ} )}{4}) + 36 0^{\circ} n

10進法形式で解を証明する

x = 0.20624 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.20624 \dots + 36 0^{\circ} n

グラフ

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