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人気のある三角関数 >

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

解

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

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 sin (x) sec (x) = 2 sin (x)

両辺から

2 sin (x)

を引く

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

因数

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

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

共通項をくくり出す

sin (x)

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

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

各部分を別個に解く

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

3 sec (x) - 2 = 0

2

を右側に移動します

3 sec (x) - 2 = 0

両辺に

2

を足す

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

簡素化

3 sec (x) = 2

3 sec (x) = 2

以下で両辺を割る

3

3 sec (x) = 2

以下で両辺を割る

3

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

簡素化

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

簡素化

\frac{3 sec ( x )}{3} : sec (x)

\frac{3 sec ( x )}{3}

共通因数を約分する:

3

= sec (x)

簡素化

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

共役で乗じる

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

累乗根の規則を適用する:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

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

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

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

以下の一般解

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

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

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

solvefor y,x=sin(y)

so l v e f or y, x = sin (y)

2sin(x/2)+sqrt(3)=0

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

2cos^2(x)+3sin(x)=0

2 cos^{2} (x) + 3 sin (x) = 0

tan (3 x) - 1 = 0

2 sin (2 x) - 1 = 0