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人気のある三角関数 >

(sin(θ))/(60)=(sin(45))/(246.26)

解

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

解

θ = 0.17314 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17314 \dots + 36 0^{\circ} n

+1

ラジアン

θ = 0.17314 \dots + 2 πn, θ = π - 0.17314 \dots + 2 πn

解答ステップ

\frac{sin ( θ )}{60} = \frac{sin ( 4 5 ^{\circ} )}{246.26}

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 ( θ )}{60} = \frac{\frac{2}{2}}{246.26}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{60} = \frac{\frac{2}{2}}{246.26}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{60} \cdot 10 = \frac{\frac{2}{2}}{246.26} \cdot 10

簡素化

\frac{sin ( θ )}{60} \cdot 10 = \frac{\frac{2}{2}}{246.26} \cdot 10

簡素化

\frac{sin ( θ )}{60} \cdot 10 : \frac{sin ( θ )}{6}

\frac{sin ( θ )}{60} \cdot 10

分数を乗じる:

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

= \frac{sin ( θ ) \cdot 10}{60}

共通因数を約分する:

10

= \frac{sin ( θ )}{6}

簡素化

\frac{\frac{2}{2}}{246.26} \cdot 10 : \frac{10 2}{492.52}

\frac{\frac{2}{2}}{246.26} \cdot 10

\frac{\frac{2}{2}}{246.26} = \frac{2}{492.52}

\frac{\frac{2}{2}}{246.26}

分数の規則を適用する:

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

= \frac{2}{2 \cdot 246.26}

数を乗じる:

2 \cdot 246.26 = 492.52

= \frac{2}{492.52}

= 10 \cdot \frac{2}{492.52}

分数を乗じる:

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

= \frac{2 \cdot 10}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

以下で両辺を乗じる:

6

\frac{sin ( θ )}{6} = \frac{10 2}{492.52}

以下で両辺を乗じる:

6

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 2}{492.52}

簡素化

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 2}{492.52}

簡素化

\frac{6 sin ( θ )}{6} : sin (θ)

\frac{6 sin ( θ )}{6}

数を割る:

\frac{6}{6} = 1

= sin (θ)

簡素化

\frac{6 \cdot 10 2}{492.52} : 0.17228 \dots

\frac{6 \cdot 10 2}{492.52}

数を乗じる:

6 \cdot 10 = 60

= \frac{60 2}{492.52}

元を10進法形式に変換する

2 = 1.41421 \dots

= \frac{60 \cdot 1.41421 \dots}{492.52}

数を乗じる:

60 \cdot 1.41421 \dots = 84.85281 \dots

= \frac{84.85281 \dots}{492.52}

数を割る:

\frac{84.85281 \dots}{492.52} = 0.17228 \dots

= 0.17228 \dots

sin (θ) = 0.17228 \dots

sin (θ) = 0.17228 \dots

sin (θ) = 0.17228 \dots

三角関数の逆数プロパティを適用する

sin (θ) = 0.17228 \dots

以下の一般解

sin (θ) = 0.17228 \dots

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

θ = arcsin (0.17228 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.17228 \dots) + 36 0^{\circ} n

θ = arcsin (0.17228 \dots) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (0.17228 \dots) + 36 0^{\circ} n

10進法形式で解を証明する

θ = 0.17314 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.17314 \dots + 36 0^{\circ} n

グラフ

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