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人気のある三角関数 >

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

解

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

解

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

+1

度

x = 0^{\circ} + 18 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

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

因数

tan (x) sec (x) - 2 tan (x) : tan (x) (sec (x) - 2)

tan (x) sec (x) - 2 tan (x)

共通項をくくり出す

tan (x)

= tan (x) (sec (x) - 2)

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

各部分を別個に解く

tan (x) = 0 or sec (x) - 2 = 0

tan (x) = 0 : x = πn

tan (x) = 0

以下の一般解

tan (x) = 0

tan (x)

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

解く

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

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

グラフ

人気の例

-9cos^2(θ)+9=17sin(θ)-8

- 9 cos^{2} (θ) + 9 = 17 sin (θ) - 8

4 tan^{2} (θ) - 9 = 0

(sin(90))/(3.37)=(sin(x))/(0.7)

\frac{sin ( 9 0 ^{\circ} )}{3.37} = \frac{sin ( x )}{0.7}

cos(x)=sqrt((1-cos(x))/2)

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

7 cos (4 x) = 6