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人気のある三角関数 >

sin^2(2x)=0.5

解

sin^{2} (2 x) = 0.5

解

x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn, x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

+1

度

x = 22. 5^{\circ} + 18 0^{\circ} n, x = 67. 5^{\circ} + 18 0^{\circ} n, x = - 22. 5^{\circ} + 18 0^{\circ} n, x = 112. 5^{\circ} + 18 0^{\circ} n

解答ステップ

sin^{2} (2 x) = 0.5

置換で解く

sin^{2} (2 x) = 0.5

仮定:

sin (2 x) = u

u^{2} = 0.5

u^{2} = 0.5 : u = 0.5, u = - 0.5

u^{2} = 0.5

x^{2} = f (a)

の場合, 解は

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

u = 0.5, u = - 0.5

代用を戻す

u = sin (2 x)

sin (2 x) = 0.5, sin (2 x) = - 0.5

sin (2 x) = 0.5, sin (2 x) = - 0.5

sin (2 x) = 0.5 : x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn

sin (2 x) = 0.5

三角関数の逆数プロパティを適用する

sin (2 x) = 0.5

以下の一般解

sin (2 x) = 0.5

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

2 x = arcsin (0.5) + 2 πn, 2 x = π - arcsin (0.5) + 2 πn

2 x = arcsin (0.5) + 2 πn, 2 x = π - arcsin (0.5) + 2 πn

解く

2 x = arcsin (0.5) + 2 πn : x = \frac{π}{8} + πn

2 x = arcsin (0.5) + 2 πn

簡素化

arcsin (0.5) + 2 πn : \frac{π}{4} + 2 πn

arcsin (0.5) + 2 πn

arcsin (0.5) = \frac{π}{4}

arcsin (0.5)

= arcsin (\frac{1}{2})

次の自明恒等式を使用する:

arcsin (\frac{1}{2}) = \frac{π}{4}

arcsin (\frac{1}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

= \frac{π}{4} + 2 πn

2 x = \frac{π}{4} + 2 πn

以下で両辺を割る

2

2 x = \frac{π}{4} + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} = \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{\frac{π}{4}}{2} + \frac{2 πn}{2} : \frac{π}{8} + πn

\frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

分数の規則を適用する:

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

= \frac{π}{4 \cdot 2}

数を乗じる:

4 \cdot 2 = 8

= \frac{π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{π}{8} + πn

x = \frac{π}{8} + πn

x = \frac{π}{8} + πn

x = \frac{π}{8} + πn

解く

2 x = π - arcsin (0.5) + 2 πn : x = \frac{π}{2} - \frac{π}{8} + πn

2 x = π - arcsin (0.5) + 2 πn

簡素化

π - arcsin (0.5) + 2 πn : π - \frac{π}{4} + 2 πn

π - arcsin (0.5) + 2 πn

arcsin (0.5) = \frac{π}{4}

arcsin (0.5)

= arcsin (\frac{1}{2})

次の自明恒等式を使用する:

arcsin (\frac{1}{2}) = \frac{π}{4}

arcsin (\frac{1}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

= π - \frac{π}{4} + 2 πn

2 x = π - \frac{π}{4} + 2 πn

以下で両辺を割る

2

2 x = π - \frac{π}{4} + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} - \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} = \frac{π}{2} - \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{π}{2} - \frac{\frac{π}{4}}{2} + \frac{2 πn}{2} : \frac{π}{2} - \frac{π}{8} + πn

\frac{π}{2} - \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

分数の規則を適用する:

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

= \frac{π}{4 \cdot 2}

数を乗じる:

4 \cdot 2 = 8

= \frac{π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{π}{2} - \frac{π}{8} + πn

x = \frac{π}{2} - \frac{π}{8} + πn

x = \frac{π}{2} - \frac{π}{8} + πn

x = \frac{π}{2} - \frac{π}{8} + πn

x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn

sin (2 x) = - 0.5 : x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

sin (2 x) = - 0.5

三角関数の逆数プロパティを適用する

sin (2 x) = - 0.5

以下の一般解

sin (2 x) = - 0.5

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

2 x = arcsin (- 0.5) + 2 πn, 2 x = π + arcsin (0.5) + 2 πn

2 x = arcsin (- 0.5) + 2 πn, 2 x = π + arcsin (0.5) + 2 πn

解く

2 x = arcsin (- 0.5) + 2 πn : x = - \frac{π}{8} + πn

2 x = arcsin (- 0.5) + 2 πn

簡素化

arcsin (- 0.5) + 2 πn : - \frac{π}{4} + 2 πn

arcsin (- 0.5) + 2 πn

arcsin (- 0.5) = - \frac{π}{4}

arcsin (- 0.5)

= arcsin (- \frac{1}{2})

次のプロパティを使用する:

arcsin (- x) = - arcsin (x)

arcsin (- \frac{1}{2}) = - arcsin (\frac{1}{2})

= - arcsin (\frac{1}{2})

次の自明恒等式を使用する:

arcsin (\frac{1}{2}) = \frac{π}{4}

arcsin (\frac{1}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{4}

= - \frac{π}{4}

= - \frac{π}{4} + 2 πn

2 x = - \frac{π}{4} + 2 πn

以下で両辺を割る

2

2 x = - \frac{π}{4} + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = - \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} = - \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

- \frac{\frac{π}{4}}{2} + \frac{2 πn}{2} : - \frac{π}{8} + πn

- \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

分数の規則を適用する:

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

= \frac{π}{4 \cdot 2}

数を乗じる:

4 \cdot 2 = 8

= \frac{π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= - \frac{π}{8} + πn

x = - \frac{π}{8} + πn

x = - \frac{π}{8} + πn

x = - \frac{π}{8} + πn

解く

2 x = π + arcsin (0.5) + 2 πn : x = \frac{π}{2} + \frac{π}{8} + πn

2 x = π + arcsin (0.5) + 2 πn

簡素化

π + arcsin (0.5) + 2 πn : π + \frac{π}{4} + 2 πn

π + arcsin (0.5) + 2 πn

arcsin (0.5) = \frac{π}{4}

arcsin (0.5)

= arcsin (\frac{1}{2})

次の自明恒等式を使用する:

arcsin (\frac{1}{2}) = \frac{π}{4}

arcsin (\frac{1}{2})

x 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 arcsin (x) 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} arcsin (x) 0^{\circ} 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ}

= \frac{π}{4}

= \frac{π}{4}

= π + \frac{π}{4} + 2 πn

2 x = π + \frac{π}{4} + 2 πn

以下で両辺を割る

2

2 x = π + \frac{π}{4} + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} + \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} = \frac{π}{2} + \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

\frac{π}{2} + \frac{\frac{π}{4}}{2} + \frac{2 πn}{2} : \frac{π}{2} + \frac{π}{8} + πn

\frac{π}{2} + \frac{\frac{π}{4}}{2} + \frac{2 πn}{2}

\frac{\frac{π}{4}}{2} = \frac{π}{8}

\frac{\frac{π}{4}}{2}

分数の規則を適用する:

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

= \frac{π}{4 \cdot 2}

数を乗じる:

4 \cdot 2 = 8

= \frac{π}{8}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

数を割る:

\frac{2}{2} = 1

= πn

= \frac{π}{2} + \frac{π}{8} + πn

x = \frac{π}{2} + \frac{π}{8} + πn

x = \frac{π}{2} + \frac{π}{8} + πn

x = \frac{π}{2} + \frac{π}{8} + πn

x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

すべての解を組み合わせる

x = \frac{π}{8} + πn, x = \frac{π}{2} - \frac{π}{8} + πn, x = - \frac{π}{8} + πn, x = \frac{π}{2} + \frac{π}{8} + πn

グラフ

人気の例

sin(x)=-1/2 sqrt(2)

sin (x) = - \frac{1}{2} 2

(6cos(x)+5sin(x))^2+11sin^2(x)=66

(6 cos (x) + 5 sin (x))^{2} + 11 sin^{2} (x) = 66

sin(θ)=(0.3924)/(cos(θ))

sin (θ) = \frac{0.3924}{cos ( θ )}

solvefor x,y=3sin(x)

so l v e f or x, y = 3 sin (x)

cos(x)=(32)/(34.54)

cos (x) = \frac{32}{34.54}