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人気のある三角関数 >

tan(3x)=1,-2pi<= x<= 2pi

解

tan (3 x) = 1, - 2 π \leq x \leq 2 π

解

x = \frac{π}{12}, x = \frac{5 π}{12}, x = \frac{3 π}{4}, x = \frac{13 π}{12}, x = \frac{17 π}{12}, x = - \frac{π}{4}, x = - \frac{7 π}{12}, x = - \frac{11 π}{12}, x = - \frac{5 π}{4}

+1

度

x = 1 5^{\circ}, x = 7 5^{\circ}, x = 13 5^{\circ}, x = 19 5^{\circ}, x = 25 5^{\circ}, x = - 4 5^{\circ}, x = - 10 5^{\circ}, x = - 16 5^{\circ}, x = - 22 5^{\circ}

解答ステップ

tan (3 x) = 1, - 2 π \leq x \leq 2 π

以下の一般解

tan (3 x) = 1

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}

3 x = \frac{π}{4} + πn

3 x = \frac{π}{4} + πn

解く

3 x = \frac{π}{4} + πn : x = \frac{π}{12} + \frac{πn}{3}

3 x = \frac{π}{4} + πn

以下で両辺を割る

3

3 x = \frac{π}{4} + πn

以下で両辺を割る

3

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

簡素化

\frac{3 x}{3} = \frac{\frac{π}{4}}{3} + \frac{πn}{3}

簡素化

\frac{3 x}{3} : x

\frac{3 x}{3}

数を割る:

\frac{3}{3} = 1

= x

簡素化

\frac{\frac{π}{4}}{3} + \frac{πn}{3} : \frac{π}{12} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} + \frac{πn}{3}

\frac{\frac{π}{4}}{3} = \frac{π}{12}

\frac{\frac{π}{4}}{3}

分数の規則を適用する:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 \cdot 3}

数を乗じる:

4 \cdot 3 = 12

= \frac{π}{12}

= \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

x = \frac{π}{12} + \frac{πn}{3}

範囲の解答

- 2 π \leq x \leq 2 π

x = \frac{π}{12}, x = \frac{5 π}{12}, x = \frac{3 π}{4}, x = \frac{13 π}{12}, x = \frac{17 π}{12}, x = - \frac{π}{4}, x = - \frac{7 π}{12}, x = - \frac{11 π}{12}, x = - \frac{5 π}{4}

グラフ

人気の例

arctan(x)= pi/(12)

arctan (x) = \frac{π}{12}

8sin^2(w)+10sin(w)+3=0

8 sin^{2} (w) + 10 sin (w) + 3 = 0

2-2cos^2(x)=2sin^2(x/2)

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

cos(2x+30)= 1/2 ,0<= x<= 360

cos (2 x + 30) = \frac{1}{2}, 0^{\circ} \leq x \leq 36 0^{\circ}

tan (θ) = \frac{43}{90}