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人気のある三角関数 >

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

解

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

解

x = 2 πn, x = π + 2 πn

+1

度

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

解答ステップ

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

両辺から

sin (x)

を引く

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

因数

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

sin (x) sec (x) - sin (x)

共通項をくくり出す

sin (x)

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

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

各部分を別個に解く

sin (x) = 0 or sec (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

sec (x) - 1 = 0 : x = 2 πn

sec (x) - 1 = 0

1

を右側に移動します

sec (x) - 1 = 0

両辺に

1

を足す

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

簡素化

sec (x) = 1

sec (x) = 1

以下の一般解

sec (x) = 1

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 = 0 + 2 πn

x = 0 + 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

すべての解を組み合わせる

x = 2 πn, x = π + 2 πn

グラフ

人気の例

cos (x) + 2 = 0

(2tan(3x))/(1-tan^2(3x))=1

\frac{2 tan ( 3 x )}{1 - tan ^{2} ( 3 x )} = 1

sin(x)=(sqrt(3))/3

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

cos(2θ)=-1/2 ,0<= θ<2pi

cos (2 θ) = - \frac{1}{2}, 0 \leq θ < 2 π

tan(x)tan(2x)=1

tan (x) tan (2 x) = 1