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人気のある三角関数 >

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

解

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

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

簡素化

sin^{3} (x) sin^{2} (x) sin (x) : sin^{6} (x)

sin^{3} (x) sin^{2} (x) sin (x)

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

sin^{3} (x) sin^{2} (x) sin (x) = sin^{3 + 2 + 1} (x)

= sin^{3 + 2 + 1} (x)

数を足す:

3 + 2 + 1 = 6

= sin^{6} (x)

sin^{6} (x) = 0

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

sin (x) = 0

解は

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

グラフ

人気の例

2cos^2(x)+1=cos^2(x)

2 cos^{2} (x) + 1 = cos^{2} (x)

sin^2(x)cos^2(x)=((1-cos^4(x)))/8

sin^{2} (x) cos^{2} (x) = \frac{( 1 - cos ^{4} ( x ) )}{8}

sin^3(x)+sin(x)=2sin^{22}(x)

sin^{3} (x) + sin (x) = 2 sin^{22} (x)

(1+tan^2(x))/(1+sec(x))=sec(x)

\frac{1 + tan ^{2} ( x )}{1 + sec ( x )} = sec (x)

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

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