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人気のある三角関数 >

sec(x)(2sin(x)+1)-2(2sin(x)+1)=0

解

sec (x) (2 sin (x) + 1) - 2 (2 sin (x) + 1) = 0

解

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

+1

度

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 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

sec (x) (2 sin (x) + 1) - 2 (2 sin (x) + 1) = 0

因数

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

sec (x) (2 sin (x) + 1) - 2 (2 sin (x) + 1)

共通項をくくり出す

(1 + 2 sin (x))

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

(1 + 2 sin (x)) (sec (x) - 2) = 0

各部分を別個に解く

1 + 2 sin (x) = 0 or sec (x) - 2 = 0

1 + 2 sin (x) = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

1 + 2 sin (x) = 0

1

を右側に移動します

1 + 2 sin (x) = 0

両辺から

1

を引く

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

簡素化

2 sin (x) = - 1

2 sin (x) = - 1

以下で両辺を割る

2

2 sin (x) = - 1

以下で両辺を割る

2

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

簡素化

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

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

以下の一般解

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

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 = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

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

sec (x) - 2 = 0

2

を右側に移動します

sec (x) - 2 = 0

両辺に

2

を足す

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

簡素化

sec (x) = 2

sec (x) = 2

以下の一般解

sec (x) = 2

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}{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 = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

グラフ

人気の例

2-3cos(x)=5+3cos(x)

2 - 3 cos (x) = 5 + 3 cos (x)

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

tan(2x)tan(x)=1

tan (2 x) tan (x) = 1

(csc^2(x))/4 =4sin^2(x)

\frac{csc ^{2} ( x )}{4} = 4 sin^{2} (x)

6sec^2(x)-3cos(x)-10=sec(x)

6 sec^{2} (x) - 3 cos (x) - 10 = sec (x)