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人気のある三角関数 >

cos(5x+40)= 3/5

解

cos (5 x + 4 0^{\circ}) = \frac{3}{5}

解

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

+1

ラジアン

x = - \frac{2 π}{45} + \frac{0.92729 \dots}{5} + \frac{2 π}{5} n, x = \frac{2 π}{5} - \frac{2 π}{45} - \frac{0.92729 \dots}{5} + \frac{2 π}{5} n

解答ステップ

cos (5 x + 4 0^{\circ}) = \frac{3}{5}

三角関数の逆数プロパティを適用する

cos (5 x + 4 0^{\circ}) = \frac{3}{5}

以下の一般解

cos (5 x + 4 0^{\circ}) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

5 x + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n, 5 x + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

5 x + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n, 5 x + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

解く

5 x + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n : x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

5 x + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n

4 0^{\circ}

を右側に移動します

5 x + 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n

両辺から

4 0^{\circ}

を引く

5 x + 4 0^{\circ} - 4 0^{\circ} = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

簡素化

5 x = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

5 x = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

以下で両辺を割る

5

5 x = arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

以下で両辺を割る

5

\frac{5 x}{5} = \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

簡素化

\frac{5 x}{5} = \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

\frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

条件のようなグループ

= \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} + \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

分数の規則を適用する:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

数を乗じる:

9 \cdot 5 = 45

= 8^{\circ}

= \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}

解く

5 x + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n : x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

5 x + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

4 0^{\circ}

を右側に移動します

5 x + 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

両辺から

4 0^{\circ}

を引く

5 x + 4 0^{\circ} - 4 0^{\circ} = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

簡素化

5 x = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

5 x = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

以下で両辺を割る

5

5 x = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n - 4 0^{\circ}

以下で両辺を割る

5

\frac{5 x}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

簡素化

\frac{5 x}{5} = 7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} : 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

7 2^{\circ} - \frac{arccos ( \frac{3}{5} )}{5} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5}

条件のようなグループ

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{4 0 ^{\circ}}{5} - \frac{arccos ( \frac{3}{5} )}{5}

\frac{4 0 ^{\circ}}{5} = 8^{\circ}

\frac{4 0 ^{\circ}}{5}

分数の規則を適用する:

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

= \frac{36 0 ^{\circ}}{9 \cdot 5}

数を乗じる:

9 \cdot 5 = 45

= 8^{\circ}

= 7 2^{\circ} + \frac{36 0 ^{\circ} n}{5} - 8^{\circ} - \frac{arccos ( \frac{3}{5} )}{5}

条件のようなグループ

= 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{arccos ( \frac{3}{5} )}{5}, x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{arccos ( \frac{3}{5} )}{5}

10進法形式で解を証明する

x = \frac{36 0 ^{\circ} n}{5} - 8^{\circ} + \frac{0.92729 \dots}{5}, x = 7 2^{\circ} - 8^{\circ} + \frac{36 0 ^{\circ} n}{5} - \frac{0.92729 \dots}{5}

グラフ

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