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人気のある三角関数 >

(sin(x))/(700)=(sin(45))/(497)

解

\frac{sin ( x )}{700} = \frac{sin ( 4 5 ^{\circ} )}{497}

解

x = 1.48048 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.48048 \dots + 36 0^{\circ} n

+1

ラジアン

x = 1.48048 \dots + 2 πn, x = π - 1.48048 \dots + 2 πn

解答ステップ

\frac{sin ( x )}{700} = \frac{sin ( 4 5 ^{\circ} )}{497}

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

sin (4 5^{\circ})

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}

= \frac{2}{2}

\frac{sin ( x )}{700} = \frac{\frac{2}{2}}{497}

以下で両辺を乗じる:

100

\frac{sin ( x )}{700} = \frac{\frac{2}{2}}{497}

以下で両辺を乗じる:

100

\frac{sin ( x )}{700} \cdot 100 = \frac{\frac{2}{2}}{497} \cdot 100

簡素化

\frac{sin ( x )}{700} \cdot 100 = \frac{\frac{2}{2}}{497} \cdot 100

簡素化

\frac{sin ( x )}{700} \cdot 100 : \frac{sin ( x )}{7}

\frac{sin ( x )}{700} \cdot 100

分数を乗じる:

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

= \frac{sin ( x ) \cdot 100}{700}

共通因数を約分する:

100

= \frac{sin ( x )}{7}

簡素化

\frac{\frac{2}{2}}{497} \cdot 100 : \frac{50 2}{497}

\frac{\frac{2}{2}}{497} \cdot 100

\frac{\frac{2}{2}}{497} = \frac{2}{994}

\frac{\frac{2}{2}}{497}

分数の規則を適用する:

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

= \frac{2}{2 \cdot 497}

数を乗じる:

2 \cdot 497 = 994

= \frac{2}{994}

= 100 \cdot \frac{2}{994}

分数を乗じる:

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

= \frac{2 \cdot 100}{994}

共通因数を約分する:

2

= \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

\frac{sin ( x )}{7} = \frac{50 2}{497}

以下で両辺を乗じる:

7

\frac{sin ( x )}{7} = \frac{50 2}{497}

以下で両辺を乗じる:

7

\frac{7 sin ( x )}{7} = \frac{7 \cdot 50 2}{497}

簡素化

\frac{7 sin ( x )}{7} = \frac{7 \cdot 50 2}{497}

簡素化

\frac{7 sin ( x )}{7} : sin (x)

\frac{7 sin ( x )}{7}

数を割る:

\frac{7}{7} = 1

= sin (x)

簡素化

\frac{7 \cdot 50 2}{497} : \frac{50 2}{71}

\frac{7 \cdot 50 2}{497}

数を乗じる:

7 \cdot 50 = 350

= \frac{350 2}{497}

共通因数を約分する:

7

= \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

sin (x) = \frac{50 2}{71}

三角関数の逆数プロパティを適用する

sin (x) = \frac{50 2}{71}

以下の一般解

sin (x) = \frac{50 2}{71}

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

x = arcsin (\frac{50 2}{71}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{50 2}{71}) + 36 0^{\circ} n

x = arcsin (\frac{50 2}{71}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{50 2}{71}) + 36 0^{\circ} n

10進法形式で解を証明する

x = 1.48048 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.48048 \dots + 36 0^{\circ} n

グラフ

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