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人気のある三角関数 >

(tan(x))(sin^2(x)-a)(sec(x)-a)=0

解

(tan (x)) (sin^{2} (x) - a) (sec (x) - a) = 0

解

x = πn, x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn, x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn, x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

解答ステップ

(tan (x)) (sin^{2} (x) - a) (sec (x) - a) = 0

各部分を別個に解く

tan (x) = 0 or sin^{2} (x) - a = 0 or sec (x) - a = 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

sin^{2} (x) - a = 0 : x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn, x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

sin^{2} (x) - a = 0

置換で解く

sin^{2} (x) - a = 0

仮定:

sin (x) = u

u^{2} - a = 0

u^{2} - a = 0 : u = a, u = - a

u^{2} - a = 0

a

を右側に移動します

u^{2} - a = 0

両辺に

a

を足す

u^{2} - a + a = 0 + a

簡素化

u^{2} = a

u^{2} = a

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

u = a, u = - a

代用を戻す

u = sin (x)

sin (x) = a, sin (x) = - a

sin (x) = a, sin (x) = - a

sin (x) = a : x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn

sin (x) = a

三角関数の逆数プロパティを適用する

sin (x) = a

以下の一般解

sin (x) = a

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn

x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn

sin (x) = - a : x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

sin (x) = - a

三角関数の逆数プロパティを適用する

sin (x) = - a

以下の一般解

sin (x) = - a

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

すべての解を組み合わせる

x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn, x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

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

sec (x) - a = 0

a

を右側に移動します

sec (x) - a = 0

両辺に

a

を足す

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

簡素化

sec (x) = a

sec (x) = a

三角関数の逆数プロパティを適用する

sec (x) = a

以下の一般解

sec (x) = a

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

x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

すべての解を組み合わせる

x = πn, x = arcsin (a) + 2 πn, x = π + arcsin (- a) + 2 πn, x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn, x = arcsec (a) + 2 πn, x = - arcsec (a) + 2 πn

グラフ

人気の例

3cos(x)+2sin(x)=sqrt(3)

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

sin(x)-1=sqrt(3)cos(x)

sin (x) - 1 = 3 cos (x)

cos(3x)=-cos(x)

cos (3 x) = - cos (x)

sqrt(3)sin(x)-((sqrt(3)sin(x))-1)=1n

3 sin (x) - ((3 sin (x)) - 1) = 1 n

3 = 3 - 3 cos (θ)