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人気のある三角関数 >

sin(3x)=0,0<= x<= 2pi

解

sin (3 x) = 0, 0 \leq x \leq 2 π

解

x = 0, x = \frac{π}{3}, x = \frac{2 π}{3}, x = π, x = \frac{4 π}{3}, x = \frac{5 π}{3}, x = 2 π

+1

度

x = 0^{\circ}, x = 6 0^{\circ}, x = 12 0^{\circ}, x = 18 0^{\circ}, x = 24 0^{\circ}, x = 30 0^{\circ}, x = 36 0^{\circ}

解答ステップ

sin (3 x) = 0, 0 \leq x \leq 2 π

以下の一般解

sin (3 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}

3 x = 0 + 2 πn, 3 x = π + 2 πn

3 x = 0 + 2 πn, 3 x = π + 2 πn

解く

3 x = 0 + 2 πn : x = \frac{2 πn}{3}

3 x = 0 + 2 πn

0 + 2 πn = 2 πn

3 x = 2 πn

以下で両辺を割る

3

3 x = 2 πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{2 πn}{3}

簡素化

x = \frac{2 πn}{3}

x = \frac{2 πn}{3}

解く

3 x = π + 2 πn : x = \frac{π}{3} + \frac{2 πn}{3}

3 x = π + 2 πn

以下で両辺を割る

3

3 x = π + 2 πn

以下で両辺を割る

3

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

簡素化

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

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

範囲の解答

0 \leq x \leq 2 π

x = 0, x = \frac{π}{3}, x = \frac{2 π}{3}, x = π, x = \frac{4 π}{3}, x = \frac{5 π}{3}, x = 2 π

グラフ

人気の例

- 4 cos (x) = 0

7cos^2(θ)-3=-2cos(θ)+2

7 cos^{2} (θ) - 3 = - 2 cos (θ) + 2

(sin(2x))/2 =sin(x)

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

sin^2(θ)+sin(θ)-6=0

sin^{2} (θ) + sin (θ) - 6 = 0

solvefor y,x+tan(xy)=0

so l v e f or y, x + tan (x y) = 0