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人気のある三角関数 >

sin(2x+60)= 1/2 ,-180<= ,x<= 180

解

sin (2 x + 60) = \frac{1}{2}, - 18 0^{\circ} \leq, x \leq 18 0^{\circ}

解

以下の解はない : x \in R

解答ステップ

sin (2 x + 60) = \frac{1}{2}, - 18 0^{\circ}, x \leq 18 0^{\circ}

以下の一般解

sin (2 x + 60) = \frac{1}{2}

sin (x)

36 0^{\circ} n

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 x + 60 = 3 0^{\circ} + 36 0^{\circ} n, 2 x + 60 = 15 0^{\circ} + 36 0^{\circ} n

2 x + 60 = 3 0^{\circ} + 36 0^{\circ} n, 2 x + 60 = 15 0^{\circ} + 36 0^{\circ} n

解く

2 x + 60 = 3 0^{\circ} + 36 0^{\circ} n : x = - 30 + 18 0^{\circ} n + 1 5^{\circ}

2 x + 60 = 3 0^{\circ} + 36 0^{\circ} n

60

を右側に移動します

2 x + 60 = 3 0^{\circ} + 36 0^{\circ} n

両辺から

60

を引く

2 x + 60 - 60 = 3 0^{\circ} + 36 0^{\circ} n - 60

簡素化

2 x = 3 0^{\circ} + 36 0^{\circ} n - 60

2 x = 3 0^{\circ} + 36 0^{\circ} n - 60

以下で両辺を割る

2

2 x = 3 0^{\circ} + 36 0^{\circ} n - 60

以下で両辺を割る

2

\frac{2 x}{2} = \frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{2}

簡素化

\frac{2 x}{2} = \frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{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{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{2} : - 30 + 18 0^{\circ} n + 1 5^{\circ}

\frac{3 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{2}

条件のようなグループ

= - \frac{60}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{3 0 ^{\circ}}{2}

\frac{60}{2} = 30

\frac{60}{2}

数を割る:

\frac{60}{2} = 30

= 30

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{3 0 ^{\circ}}{2} = 1 5^{\circ}

\frac{3 0 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= 1 5^{\circ}

= - 30 + 18 0^{\circ} n + 1 5^{\circ}

x = - 30 + 18 0^{\circ} n + 1 5^{\circ}

x = - 30 + 18 0^{\circ} n + 1 5^{\circ}

x = - 30 + 18 0^{\circ} n + 1 5^{\circ}

解く

2 x + 60 = 15 0^{\circ} + 36 0^{\circ} n : x = - 30 + 18 0^{\circ} n + 7 5^{\circ}

2 x + 60 = 15 0^{\circ} + 36 0^{\circ} n

60

を右側に移動します

2 x + 60 = 15 0^{\circ} + 36 0^{\circ} n

両辺から

60

を引く

2 x + 60 - 60 = 15 0^{\circ} + 36 0^{\circ} n - 60

簡素化

2 x = 15 0^{\circ} + 36 0^{\circ} n - 60

2 x = 15 0^{\circ} + 36 0^{\circ} n - 60

以下で両辺を割る

2

2 x = 15 0^{\circ} + 36 0^{\circ} n - 60

以下で両辺を割る

2

\frac{2 x}{2} = \frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{2}

簡素化

\frac{2 x}{2} = \frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{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{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{2} : - 30 + 18 0^{\circ} n + 7 5^{\circ}

\frac{15 0 ^{\circ}}{2} + \frac{36 0 ^{\circ} n}{2} - \frac{60}{2}

条件のようなグループ

= - \frac{60}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{15 0 ^{\circ}}{2}

\frac{60}{2} = 30

\frac{60}{2}

数を割る:

\frac{60}{2} = 30

= 30

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

数を割る:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{15 0 ^{\circ}}{2} = 7 5^{\circ}

\frac{15 0 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{90 0 ^{\circ}}{6 \cdot 2}

数を乗じる:

6 \cdot 2 = 12

= 7 5^{\circ}

= - 30 + 18 0^{\circ} n + 7 5^{\circ}

x = - 30 + 18 0^{\circ} n + 7 5^{\circ}

x = - 30 + 18 0^{\circ} n + 7 5^{\circ}

x = - 30 + 18 0^{\circ} n + 7 5^{\circ}

x = - 30 + 18 0^{\circ} n + 1 5^{\circ}, x = - 30 + 18 0^{\circ} n + 7 5^{\circ}

範囲の解答

- 18 0^{\circ}

以下の解はない : x \in R

グラフ

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