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人気のある三角関数 >

0.56=tan^2(45+x/2)

解

0.56 = tan^{2} (4 5^{\circ} + \frac{x}{2})

解

x = 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

ラジアン

x = 2 \cdot 0.64243 \dots - \frac{π}{2} + 2 πn, x = - 2 \cdot 0.64243 \dots - \frac{π}{2} + 2 πn

解答ステップ

0.56 = tan^{2} (4 5^{\circ} + \frac{x}{2})

辺を交換する

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 0.56

置換で解く

tan^{2} (4 5^{\circ} + \frac{x}{2}) = 0.56

仮定:

tan (4 5^{\circ} + \frac{x}{2}) = u

u^{2} = 0.56

u^{2} = 0.56 : u = 0.56, u = - 0.56

u^{2} = 0.56

x^{2} = f (a)

の場合, 解は

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

u = 0.56, u = - 0.56

代用を戻す

u = tan (4 5^{\circ} + \frac{x}{2})

tan (4 5^{\circ} + \frac{x}{2}) = 0.56, tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56, tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (4 5^{\circ} + \frac{x}{2}) = 0.56 : x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

三角関数の逆数プロパティを適用する

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

以下の一般解

tan (4 5^{\circ} + \frac{x}{2}) = 0.56

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

解く

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n : x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

4 5^{\circ}

を右側に移動します

4 5^{\circ} + \frac{x}{2} = arctan (0.56) + 18 0^{\circ} n

両辺から

4 5^{\circ}

を引く

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

簡素化

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

以下で両辺を乗じる:

2

\frac{x}{2} = arctan (0.56) + 18 0^{\circ} n - 4 5^{\circ}

以下で両辺を乗じる:

2

\frac{2 x}{2} = 2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

簡素化

\frac{2 x}{2} = 2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (0.56) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

分数を乗じる:

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

= 9 0^{\circ}

共通因数を約分する:

2

= 9 0^{\circ}

= 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56 : x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

三角関数の逆数プロパティを適用する

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

以下の一般解

tan (4 5^{\circ} + \frac{x}{2}) = - 0.56

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

解く

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n : x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (- 0.56) + 18 0^{\circ} n

簡素化

arctan (- 0.56) + 18 0^{\circ} n : - arctan (\frac{14}{5}) + 18 0^{\circ} n

arctan (- 0.56) + 18 0^{\circ} n

arctan (- 0.56) = - arctan (\frac{14}{5})

arctan (- 0.56)

= arctan (- \frac{14}{25})

次のプロパティを使用する:

arctan (- x) = - arctan (x)

arctan (- \frac{14}{25}) = - arctan (\frac{14}{25})

= - arctan (\frac{14}{25})

= - arctan (\frac{14}{5})

= - arctan (\frac{14}{5}) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n

4 5^{\circ}

を右側に移動します

4 5^{\circ} + \frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n

両辺から

4 5^{\circ}

を引く

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

簡素化

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

以下で両辺を乗じる:

2

\frac{x}{2} = - arctan (\frac{14}{5}) + 18 0^{\circ} n - 4 5^{\circ}

以下で両辺を乗じる:

2

\frac{2 x}{2} = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

簡素化

\frac{2 x}{2} = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

- 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

分数を乗じる:

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

= 9 0^{\circ}

共通因数を約分する:

2

= 9 0^{\circ}

= - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

すべての解を組み合わせる

x = 2 arctan (0.56) + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 arctan (\frac{14}{5}) + 36 0^{\circ} n - 9 0^{\circ}

10進法形式で解を証明する

x = 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}, x = - 2 \cdot 0.64243 \dots + 36 0^{\circ} n - 9 0^{\circ}

グラフ

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