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人気のある三角関数 >

(sin(θ))/(60)=(sin(80))/(280.87)

解

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

解

θ = 0.21196 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21196 \dots + 36 0^{\circ} n

+1

ラジアン

θ = 0.21196 \dots + 2 πn, θ = π - 0.21196 \dots + 2 πn

解答ステップ

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{60} = \frac{sin ( 8 0 ^{\circ} )}{280.87}

以下で両辺を乗じる:

10

\frac{sin ( θ )}{60} \cdot 10 = \frac{sin ( 8 0 ^{\circ} )}{280.87} \cdot 10

簡素化

\frac{sin ( θ )}{60} \cdot 10 = \frac{sin ( 8 0 ^{\circ} )}{280.87} \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{sin ( 8 0 ^{\circ} )}{280.87} \cdot 10 : \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

\frac{sin ( 8 0 ^{\circ} )}{280.87} \cdot 10

分数を乗じる:

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

= \frac{sin ( 8 0 ^{\circ} ) \cdot 10}{280.87}

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

以下で両辺を乗じる:

6

\frac{sin ( θ )}{6} = \frac{10 sin ( 8 0 ^{\circ} )}{280.87}

以下で両辺を乗じる:

6

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 sin ( 8 0 ^{\circ} )}{280.87}

簡素化

\frac{6 sin ( θ )}{6} = \frac{6 \cdot 10 sin ( 8 0 ^{\circ} )}{280.87}

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 sin ( 8 0 ^{\circ} )}{280.87} : \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

\frac{6 \cdot 10 sin ( 8 0 ^{\circ} )}{280.87}

数を乗じる:

6 \cdot 10 = 60

= \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

三角関数の逆数プロパティを適用する

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

以下の一般解

sin (θ) = \frac{60 sin ( 8 0 ^{\circ} )}{280.87}

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

θ = arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n

θ = arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n, θ = 18 0^{\circ} - arcsin (\frac{60 sin ( 8 0 ^{\circ} )}{280.87}) + 36 0^{\circ} n

10進法形式で解を証明する

θ = 0.21196 \dots + 36 0^{\circ} n, θ = 18 0^{\circ} - 0.21196 \dots + 36 0^{\circ} n

グラフ

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