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人気のある三角関数 >

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

解

2 sin (x) sec (x) - 23 sin (x) = 0

解

x = 2 πn, x = π + 2 πn, x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn

+1

度

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n, x = 54.73561 \dots^{\circ} + 36 0^{\circ} n, x = 305.26438 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

2 sin (x) sec (x) - 23 sin (x) = 0

因数

2 sin (x) sec (x) - 23 sin (x) : 2 sin (x) (sec (x) - 3)

2 sin (x) sec (x) - 23 sin (x)

共通項をくくり出す

2 sin (x)

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

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

各部分を別個に解く

sin (x) = 0 or sec (x) - 3 = 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

sec (x) - 3 = 0 : x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

sec (x) - 3 = 0

3

を右側に移動します

sec (x) - 3 = 0

両辺に

3

を足す

sec (x) - 3 + 3 = 0 + 3

簡素化

sec (x) = 3

sec (x) = 3

三角関数の逆数プロパティを適用する

sec (x) = 3

以下の一般解

sec (x) = 3

sec (x) = a \Rightarrow x = arcsec (a) + 2 πn, x = 2 π - arcsec (a) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn, x = arcsec (3) + 2 πn, x = 2 π - arcsec (3) + 2 πn

10進法形式で解を証明する

x = 2 πn, x = π + 2 πn, x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn

グラフ

人気の例

cot(a)sec(a)=cos(a)

cot (a) sec (a) = cos (a)

4sin^2(x)=4cos(x)+1

4 sin^{2} (x) = 4 cos (x) + 1

2tan^2(x)+3tan(x)-2=0

2 tan^{2} (x) + 3 tan (x) - 2 = 0

sin(x)=-3cos(x)

sin (x) = - 3 cos (x)

2cos(t)*sin(t)=cos(t)

2 cos (t) \cdot sin (t) = cos (t)