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人気のある三角関数 >

sqrt(3)tan(x)-2sin(x)=0

解

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

解

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 3 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

解答ステップ

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

サイン, コサインで表わす

- 2 sin (x) + 3 tan (x)

基本的な三角関数の公式を使用する:

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

= - 2 sin (x) + 3 \frac{sin ( x )}{cos ( x )}

簡素化

- 2 sin (x) + 3 \frac{sin ( x )}{cos ( x )} : \frac{- 2 sin ( x ) cos ( x ) + 3 sin ( x )}{cos ( x )}

- 2 sin (x) + 3 \frac{sin ( x )}{cos ( x )}

乗じる

3 \frac{sin ( x )}{cos ( x )} : \frac{3 sin ( x )}{cos ( x )}

3 \frac{sin ( x )}{cos ( x )}

分数を乗じる:

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

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

= - 2 sin (x) + \frac{3 sin ( x )}{cos ( x )}

元を分数に変換する:

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

= - \frac{2 sin ( x ) cos ( x )}{cos ( x )} + \frac{sin ( x ) 3}{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{- 2 sin ( x ) cos ( x ) + sin ( x ) 3}{cos ( x )}

= \frac{- 2 sin ( x ) cos ( x ) + 3 sin ( x )}{cos ( x )}

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

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

sin (x) 3 - 2 cos (x) sin (x) = 0

因数

sin (x) 3 - 2 cos (x) sin (x) : sin (x) (3 - 2 cos (x))

sin (x) 3 - 2 cos (x) sin (x)

共通項をくくり出す

sin (x)

= sin (x) (3 - 2 cos (x))

sin (x) (3 - 2 cos (x)) = 0

各部分を別個に解く

sin (x) = 0 or 3 - 2 cos (x) = 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

3 - 2 cos (x) = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

3 - 2 cos (x) = 0

3

を右側に移動します

3 - 2 cos (x) = 0

両辺から

3

を引く

3 - 2 cos (x) - 3 = 0 - 3

簡素化

- 2 cos (x) = - 3

- 2 cos (x) = - 3

以下で両辺を割る

- 2

- 2 cos (x) = - 3

以下で両辺を割る

- 2

\frac{- 2 cos ( x )}{- 2} = \frac{- 3}{- 2}

簡素化

cos (x) = \frac{3}{2}

cos (x) = \frac{3}{2}

以下の一般解

cos (x) = \frac{3}{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}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

グラフ

人気の例

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

2 sin^{2} (2 x) - cos (2 x) - 1 = 0

cos(x)+sqrt(3)sin(x)=2

cos (x) + 3 sin (x) = 2

cos(θ)=(sqrt(11))/5

cos (θ) = \frac{11}{5}

4cos^2(x)tan(x)-tan(x)=0

4 cos^{2} (x) tan (x) - tan (x) = 0

2cos(pi/4-3x)=sqrt(2)

2 cos (\frac{π}{4} - 3 x) = 2