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人気のある三角関数 >

(sin(60))/(174.36)=(sin(x))/(200)

解

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

解

x = 1.45563 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.45563 \dots + 36 0^{\circ} n

+1

ラジアン

x = 1.45563 \dots + 2 πn, x = π - 1.45563 \dots + 2 πn

解答ステップ

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

次の自明恒等式を使用する:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

= \frac{3}{2}

\frac{\frac{3}{2}}{174.36} = \frac{sin ( x )}{200}

辺を交換する

\frac{sin ( x )}{200} = \frac{\frac{3}{2}}{174.36}

以下で両辺を乗じる:

100

\frac{sin ( x )}{200} = \frac{\frac{3}{2}}{174.36}

以下で両辺を乗じる:

100

\frac{sin ( x )}{200} \cdot 100 = \frac{\frac{3}{2}}{174.36} \cdot 100

簡素化

\frac{sin ( x )}{200} \cdot 100 = \frac{\frac{3}{2}}{174.36} \cdot 100

簡素化

\frac{sin ( x )}{200} \cdot 100 : \frac{sin ( x )}{2}

\frac{sin ( x )}{200} \cdot 100

分数を乗じる:

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

= \frac{sin ( x ) \cdot 100}{200}

共通因数を約分する:

100

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

簡素化

\frac{\frac{3}{2}}{174.36} \cdot 100 : \frac{100 3}{348.72}

\frac{\frac{3}{2}}{174.36} \cdot 100

\frac{\frac{3}{2}}{174.36} = \frac{3}{348.72}

\frac{\frac{3}{2}}{174.36}

分数の規則を適用する:

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

= \frac{3}{2 \cdot 174.36}

数を乗じる:

2 \cdot 174.36 = 348.72

= \frac{3}{348.72}

= 100 \cdot \frac{3}{348.72}

分数を乗じる:

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

= \frac{3 \cdot 100}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

以下で両辺を乗じる:

2

\frac{sin ( x )}{2} = \frac{100 3}{348.72}

以下で両辺を乗じる:

2

\frac{2 sin ( x )}{2} = \frac{2 \cdot 100 3}{348.72}

簡素化

\frac{2 sin ( x )}{2} = \frac{2 \cdot 100 3}{348.72}

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{2 \cdot 100 3}{348.72} : 0.99337 \dots

\frac{2 \cdot 100 3}{348.72}

数を乗じる:

2 \cdot 100 = 200

= \frac{200 3}{348.72}

元を10進法形式に変換する

3 = 1.73205 \dots

= \frac{200 \cdot 1.73205 \dots}{348.72}

数を乗じる:

200 \cdot 1.73205 \dots = 346.41016 \dots

= \frac{346.41016 \dots}{348.72}

数を割る:

\frac{346.41016 \dots}{348.72} = 0.99337 \dots

= 0.99337 \dots

sin (x) = 0.99337 \dots

sin (x) = 0.99337 \dots

sin (x) = 0.99337 \dots

三角関数の逆数プロパティを適用する

sin (x) = 0.99337 \dots

以下の一般解

sin (x) = 0.99337 \dots

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

x = arcsin (0.99337 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.99337 \dots) + 36 0^{\circ} n

x = arcsin (0.99337 \dots) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (0.99337 \dots) + 36 0^{\circ} n

10進法形式で解を証明する

x = 1.45563 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 1.45563 \dots + 36 0^{\circ} n

グラフ

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