ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある三角関数 >

6sin(4x)+4=5,0<= x<= 2pi

解

6 sin (4 x) + 4 = 5, 0 \leq x \leq 2 π

解

x = \frac{0.16744 \dots}{4}, x = \frac{π - 0.16744 \dots}{4}, x = \frac{0.16744 \dots + 2 π}{4}, x = \frac{3 π - 0.16744 \dots}{4}, x = \frac{0.16744 \dots + 4 π}{4}, x = \frac{5 π - 0.16744 \dots}{4}, x = \frac{0.16744 \dots + 6 π}{4}, x = \frac{7 π - 0.16744 \dots}{4}

+1

度

x = 2.39851 \dots^{\circ}, x = 42.60148 \dots^{\circ}, x = 92.39851 \dots^{\circ}, x = 132.60148 \dots^{\circ}, x = 182.39851 \dots^{\circ}, x = 222.60148 \dots^{\circ}, x = 272.39851 \dots^{\circ}, x = 312.60148 \dots^{\circ}

解答ステップ

6 sin (4 x) + 4 = 5, 0 \leq x \leq 2 π

4

を右側に移動します

6 sin (4 x) + 4 = 5

両辺から

4

を引く

6 sin (4 x) + 4 - 4 = 5 - 4

簡素化

6 sin (4 x) = 1

6 sin (4 x) = 1

以下で両辺を割る

6

6 sin (4 x) = 1

以下で両辺を割る

6

\frac{6 sin ( 4 x )}{6} = \frac{1}{6}

簡素化

sin (4 x) = \frac{1}{6}

sin (4 x) = \frac{1}{6}

三角関数の逆数プロパティを適用する

sin (4 x) = \frac{1}{6}

以下の一般解

sin (4 x) = \frac{1}{6}

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

4 x = arcsin (\frac{1}{6}) + 2 πn, 4 x = π - arcsin (\frac{1}{6}) + 2 πn

4 x = arcsin (\frac{1}{6}) + 2 πn, 4 x = π - arcsin (\frac{1}{6}) + 2 πn

解く

4 x = arcsin (\frac{1}{6}) + 2 πn : x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

4 x = arcsin (\frac{1}{6}) + 2 πn

以下で両辺を割る

4

4 x = arcsin (\frac{1}{6}) + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{2 πn}{4}

簡素化

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

解く

4 x = π - arcsin (\frac{1}{6}) + 2 πn : x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

4 x = π - arcsin (\frac{1}{6}) + 2 πn

以下で両辺を割る

4

4 x = π - arcsin (\frac{1}{6}) + 2 πn

以下で両辺を割る

4

\frac{4 x}{4} = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{2 πn}{4}

簡素化

x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

x = \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}, x = \frac{π}{4} - \frac{arcsin ( \frac{1}{6} )}{4} + \frac{πn}{2}

範囲の解答

0 \leq x \leq 2 π

x = \frac{arcsin ( \frac{1}{6} )}{4}, x = \frac{π - arcsin ( \frac{1}{6} )}{4}, x = \frac{arcsin ( \frac{1}{6} ) + 2 π}{4}, x = \frac{3 π - arcsin ( \frac{1}{6} )}{4}, x = \frac{arcsin ( \frac{1}{6} ) + 4 π}{4}, x = \frac{5 π - arcsin ( \frac{1}{6} )}{4}, x = \frac{arcsin ( \frac{1}{6} ) + 6 π}{4}, x = \frac{7 π - arcsin ( \frac{1}{6} )}{4}

10進法形式で解を証明する

x = \frac{0.16744 \dots}{4}, x = \frac{π - 0.16744 \dots}{4}, x = \frac{0.16744 \dots + 2 π}{4}, x = \frac{3 π - 0.16744 \dots}{4}, x = \frac{0.16744 \dots + 4 π}{4}, x = \frac{5 π - 0.16744 \dots}{4}, x = \frac{0.16744 \dots + 6 π}{4}, x = \frac{7 π - 0.16744 \dots}{4}

グラフ

人気の例

sqrt(3)tan(x)=3

3 tan (x) = 3

solvefor t,y=sin(t)

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

sec^2(q)=sec(q)+2

sec^{2} (q) = sec (q) + 2

sin (θ) + 4 = 3

cos (3 x) = \frac{1}{3}