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人気のある三角関数 >

sin(x)= 1/2 tan(x)

解

sin (x) = \frac{1}{2} tan (x)

解

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

解答ステップ

sin (x) = \frac{1}{2} tan (x)

両辺から

\frac{1}{2} tan (x)

を引く

sin (x) - \frac{1}{2} tan (x) = 0

簡素化

sin (x) - \frac{1}{2} tan (x) : \frac{2 sin ( x ) - tan ( x )}{2}

sin (x) - \frac{1}{2} tan (x)

\frac{1}{2} tan (x) = \frac{tan ( x )}{2}

\frac{1}{2} tan (x)

分数を乗じる:

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

= \frac{1 \cdot tan ( x )}{2}

乗算:

1 \cdot tan (x) = tan (x)

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

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

元を分数に変換する:

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

= \frac{sin ( x ) \cdot 2}{2} - \frac{tan ( x )}{2}

分母が等しいので, 分数を組み合わせる:

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

= \frac{sin ( x ) \cdot 2 - tan ( x )}{2}

\frac{2 sin ( x ) - tan ( x )}{2} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

2 sin (x) - tan (x) = 0

サイン, コサインで表わす

- tan (x) + 2 sin (x)

基本的な三角関数の公式を使用する:

tan (x) = \frac{sin ( x )}{cos ( x )}

= - \frac{sin ( x )}{cos ( x )} + 2 sin (x)

簡素化

- \frac{sin ( x )}{cos ( x )} + 2 sin (x) : \frac{- sin ( x ) + 2 sin ( x ) cos ( x )}{cos ( x )}

- \frac{sin ( x )}{cos ( x )} + 2 sin (x)

元を分数に変換する:

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

= - \frac{sin ( x )}{cos ( x )} + \frac{2 sin ( x ) cos ( x )}{cos ( x )}

分母が等しいので, 分数を組み合わせる:

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

= \frac{- sin ( x ) + 2 sin ( x ) cos ( x )}{cos ( x )}

= \frac{- sin ( x ) + 2 sin ( x ) cos ( x )}{cos ( x )}

\frac{- sin ( x ) + 2 cos ( x ) sin ( x )}{cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

- sin (x) + 2 cos (x) sin (x) = 0

因数

- sin (x) + 2 cos (x) sin (x) : sin (x) (2 cos (x) - 1)

- sin (x) + 2 cos (x) sin (x)

共通項をくくり出す

sin (x)

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

sin (x) (2 cos (x) - 1) = 0

各部分を別個に解く

sin (x) = 0 or 2 cos (x) - 1 = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 0

以下の一般解

sin (x) = 0

sin (x)

2 πn

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}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解く

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

2 cos (x) - 1 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

2 cos (x) - 1 = 0

1

を右側に移動します

2 cos (x) - 1 = 0

両辺に

1

を足す

2 cos (x) - 1 + 1 = 0 + 1

簡素化

2 cos (x) = 1

2 cos (x) = 1

以下で両辺を割る

2

2 cos (x) = 1

以下で両辺を割る

2

\frac{2 cos ( x )}{2} = \frac{1}{2}

簡素化

cos (x) = \frac{1}{2}

cos (x) = \frac{1}{2}

以下の一般解

cos (x) = \frac{1}{2}

cos (x)

2 πn

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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

グラフ

人気の例

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solvefor x,cos(x)=sin(x)

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