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人気のある三角関数 >

8cos(x+10)=5

解

8 cos (x + 1 0^{\circ}) = 5

解

x = 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}

+1

ラジアン

x = 0.89566 \dots - \frac{π}{18} + 2 πn, x = 2 π - 0.89566 \dots - \frac{π}{18} + 2 πn

解答ステップ

8 cos (x + 1 0^{\circ}) = 5

以下で両辺を割る

8

8 cos (x + 1 0^{\circ}) = 5

以下で両辺を割る

8

\frac{8 cos ( x + 1 0 ^{\circ} )}{8} = \frac{5}{8}

簡素化

cos (x + 1 0^{\circ}) = \frac{5}{8}

cos (x + 1 0^{\circ}) = \frac{5}{8}

三角関数の逆数プロパティを適用する

cos (x + 1 0^{\circ}) = \frac{5}{8}

以下の一般解

cos (x + 1 0^{\circ}) = \frac{5}{8}

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

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n, x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n, x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

解く

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n : x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n

1 0^{\circ}

を右側に移動します

x + 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n

両辺から

1 0^{\circ}

を引く

x + 1 0^{\circ} - 1 0^{\circ} = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

簡素化

x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

解く

x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n : x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

1 0^{\circ}

を右側に移動します

x + 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n

両辺から

1 0^{\circ}

を引く

x + 1 0^{\circ} - 1 0^{\circ} = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

簡素化

x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

x = arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - arccos (\frac{5}{8}) + 36 0^{\circ} n - 1 0^{\circ}

10進法形式で解を証明する

x = 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}, x = 36 0^{\circ} - 0.89566 \dots + 36 0^{\circ} n - 1 0^{\circ}

グラフ

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