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人気のある三角関数 >

(sin(x))/(120)=(sin(60))/(300)

解

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

解

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

+1

ラジアン

x = 0.35374 \dots + 2 πn, x = π - 0.35374 \dots + 2 πn

解答ステップ

\frac{sin ( x )}{120} = \frac{sin ( 6 0 ^{\circ} )}{300}

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{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

以下で両辺を乗じる:

100

\frac{sin ( x )}{120} = \frac{\frac{3}{2}}{300}

以下で両辺を乗じる:

100

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

簡素化

\frac{sin ( x )}{120} \cdot 100 = \frac{\frac{3}{2}}{300} \cdot 100

簡素化

\frac{sin ( x )}{120} \cdot 100 : \frac{5 sin ( x )}{6}

\frac{sin ( x )}{120} \cdot 100

分数を乗じる:

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

= \frac{sin ( x ) \cdot 100}{120}

共通因数を約分する:

20

= \frac{5 sin ( x )}{6}

簡素化

\frac{\frac{3}{2}}{300} \cdot 100 : \frac{3}{6}

\frac{\frac{3}{2}}{300} \cdot 100

\frac{\frac{3}{2}}{300} = \frac{3}{600}

\frac{\frac{3}{2}}{300}

分数の規則を適用する:

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

= \frac{3}{2 \cdot 300}

数を乗じる:

2 \cdot 300 = 600

= \frac{3}{600}

= 100 \cdot \frac{3}{600}

分数を乗じる:

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

= \frac{3 \cdot 100}{600}

共通因数を約分する:

100

= \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

\frac{5 sin ( x )}{6} = \frac{3}{6}

以下で両辺を乗じる:

6

\frac{5 sin ( x )}{6} = \frac{3}{6}

以下で両辺を乗じる:

6

\frac{6 \cdot 5 sin ( x )}{6} = \frac{6 3}{6}

簡素化

5 sin (x) = 3

5 sin (x) = 3

以下で両辺を割る

5

5 sin (x) = 3

以下で両辺を割る

5

\frac{5 sin ( x )}{5} = \frac{3}{5}

簡素化

sin (x) = \frac{3}{5}

sin (x) = \frac{3}{5}

三角関数の逆数プロパティを適用する

sin (x) = \frac{3}{5}

以下の一般解

sin (x) = \frac{3}{5}

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

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

x = arcsin (\frac{3}{5}) + 36 0^{\circ} n, x = 18 0^{\circ} - arcsin (\frac{3}{5}) + 36 0^{\circ} n

10進法形式で解を証明する

x = 0.35374 \dots + 36 0^{\circ} n, x = 18 0^{\circ} - 0.35374 \dots + 36 0^{\circ} n

グラフ

人気の例

8sin(θ)+15cos(θ)=0

8 sin (θ) + 15 cos (θ) = 0

sin (t) = \frac{3}{7}

cos(2x-1)=sin(3x+6)

cos (2 x - 1) = sin (3 x + 6)

(sin(b))/(300)=(sin(49))/(500)

\frac{sin ( b )}{300} = \frac{sin ( 4 9 ^{\circ} )}{500}

sin(θ)=cos(2θ+60)

sin (θ) = cos (2 θ + 6 0^{\circ})