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人気のある三角関数 >

sin(2θ)= 1/2 ,0<= θ<= 2pi

解

sin (2 θ) = \frac{1}{2}, 0 \leq θ \leq 2 π

解

θ = \frac{π}{12}, θ = \frac{5 π}{12}, θ = \frac{13 π}{12}, θ = \frac{17 π}{12}

+1

度

θ = 1 5^{\circ}, θ = 7 5^{\circ}, θ = 19 5^{\circ}, θ = 25 5^{\circ}

解答ステップ

sin (2 θ) = \frac{1}{2}, 0 \leq θ \leq 2 π

以下の一般解

sin (2 θ) = \frac{1}{2}

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}

2 θ = \frac{π}{6} + 2 πn, 2 θ = \frac{5 π}{6} + 2 πn

2 θ = \frac{π}{6} + 2 πn, 2 θ = \frac{5 π}{6} + 2 πn

解く

2 θ = \frac{π}{6} + 2 πn : θ = \frac{π}{12} + πn

2 θ = \frac{π}{6} + 2 πn

以下で両辺を割る

2

2 θ = \frac{π}{6} + 2 πn

以下で両辺を割る

2

\frac{2 θ}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 θ}{2} = \frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数を割る:

\frac{2}{2} = 1

= θ

簡素化

\frac{\frac{π}{6}}{2} + \frac{2 πn}{2} : \frac{π}{12} + πn

\frac{\frac{π}{6}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{6}}{2} = \frac{π}{12}

\frac{\frac{π}{6}}{2}

分数の規則を適用する:

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

= \frac{π}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= \frac{π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{π}{12} + πn

θ = \frac{π}{12} + πn

θ = \frac{π}{12} + πn

θ = \frac{π}{12} + πn

解く

2 θ = \frac{5 π}{6} + 2 πn : θ = \frac{5 π}{12} + πn

2 θ = \frac{5 π}{6} + 2 πn

以下で両辺を割る

2

2 θ = \frac{5 π}{6} + 2 πn

以下で両辺を割る

2

\frac{2 θ}{2} = \frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 θ}{2} = \frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数を割る:

\frac{2}{2} = 1

= θ

簡素化

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2} : \frac{5 π}{12} + πn

\frac{\frac{5 π}{6}}{2} + \frac{2 πn}{2}

\frac{\frac{5 π}{6}}{2} = \frac{5 π}{12}

\frac{\frac{5 π}{6}}{2}

分数の規則を適用する:

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

= \frac{5 π}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= \frac{5 π}{12}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{5 π}{12} + πn

θ = \frac{π}{12} + πn, θ = \frac{5 π}{12} + πn

範囲の解答

0 \leq θ \leq 2 π

θ = \frac{π}{12}, θ = \frac{5 π}{12}, θ = \frac{13 π}{12}, θ = \frac{17 π}{12}

グラフ

人気の例

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

-12cos^2(θ)+3=-3

sqrt(3)sec(x)+sec(x)cot(x)=0