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人気のある三角関数 >

1715/70 =tan(45+θ/2)

解

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

解

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

+1

ラジアン

θ = 2 \cdot 1.53000 \dots - \frac{π}{2} + 2 πn

解答ステップ

\frac{1715}{70} = tan (4 5^{\circ} + \frac{θ}{2})

辺を交換する

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{1715}{70}

共通因数を約分する:

35

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

三角関数の逆数プロパティを適用する

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

以下の一般解

tan (4 5^{\circ} + \frac{θ}{2}) = \frac{49}{2}

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

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

解く

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n : θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

4 5^{\circ}

を右側に移動します

4 5^{\circ} + \frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n

両辺から

4 5^{\circ}

を引く

4 5^{\circ} + \frac{θ}{2} - 4 5^{\circ} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

簡素化

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

以下で両辺を乗じる:

2

\frac{θ}{2} = arctan (\frac{49}{2}) + 18 0^{\circ} n - 4 5^{\circ}

以下で両辺を乗じる:

2

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

簡素化

\frac{2 θ}{2} = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

簡素化

\frac{2 θ}{2} : θ

\frac{2 θ}{2}

数を割る:

\frac{2}{2} = 1

= θ

簡素化

2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

2 arctan (\frac{49}{2}) + 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{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

θ = 2 arctan (\frac{49}{2}) + 36 0^{\circ} n - 9 0^{\circ}

10進法形式で解を証明する

θ = 2 \cdot 1.53000 \dots + 36 0^{\circ} n - 9 0^{\circ}

グラフ

人気の例

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885cos(θ)-70=cos(250)

885 cos (θ) - 70 = cos (25 0^{\circ})

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