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人気のある三角関数 >

-3sqrt(3)+7csc(θ/5+23)=5sqrt(3)

解

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

解

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

+1

ラジアン

θ = 5 \cdot 0.52959 \dots - \frac{23 π}{36} + 10 πn, θ = 5 π - 5 \cdot 0.52959 \dots - \frac{23 π}{36} + 10 πn

解答ステップ

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

33

を右側に移動します

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) = 53

両辺に

33

を足す

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 = 53 + 33

簡素化

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 = 53 + 33

簡素化

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33 : 7 csc (\frac{θ}{5} + 2 3^{\circ})

- 33 + 7 csc (\frac{θ}{5} + 2 3^{\circ}) + 33

類似した元を足す:

- 33 + 33 = 0

= 7 csc (\frac{θ}{5} + 2 3^{\circ})

簡素化

53 + 33 : 83

53 + 33

類似した元を足す:

53 + 33 = 83

= 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

以下で両辺を割る

7

7 csc (\frac{θ}{5} + 2 3^{\circ}) = 83

以下で両辺を割る

7

\frac{7 csc ( \frac{θ}{5} + 2 3 ^{\circ} )}{7} = \frac{8 3}{7}

簡素化

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

三角関数の逆数プロパティを適用する

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

以下の一般解

csc (\frac{θ}{5} + 2 3^{\circ}) = \frac{8 3}{7}

csc (x) = a \Rightarrow x = arccsc (a) + 36 0^{\circ} n, x = 18 0^{\circ} - arccsc (a) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n, \frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

解く

\frac{θ}{5} + 2 3^{\circ} = arccsc (\frac{8 3}{7}) + 36 0^{\circ} n : θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

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

2 3^{\circ}

を右側に移動します

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

両辺から

2 3^{\circ}

を引く

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

簡素化

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

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

以下で両辺を乗じる:

5

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

以下で両辺を乗じる:

5

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

簡素化

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

簡素化

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数を割る:

\frac{5}{5} = 1

= θ

簡素化

5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ} : 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

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

5 \cdot 36 0^{\circ} n = 180 0^{\circ} n

5 \cdot 36 0^{\circ} n

数を乗じる:

5 \cdot 2 = 10

= 180 0^{\circ} n

5 \cdot 2 3^{\circ} = 11 5^{\circ}

5 \cdot 2 3^{\circ}

分数を乗じる:

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

= 11 5^{\circ}

数を乗じる:

23 \cdot 5 = 115

= 11 5^{\circ}

共通因数を約分する:

5

= 11 5^{\circ}

= 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

解く

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n : θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

2 3^{\circ}

を右側に移動します

\frac{θ}{5} + 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n

両辺から

2 3^{\circ}

を引く

\frac{θ}{5} + 2 3^{\circ} - 2 3^{\circ} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

簡素化

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

以下で両辺を乗じる:

5

\frac{θ}{5} = 18 0^{\circ} - arccsc (\frac{8 3}{7}) + 36 0^{\circ} n - 2 3^{\circ}

以下で両辺を乗じる:

5

\frac{5 θ}{5} = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

簡素化

\frac{5 θ}{5} = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

簡素化

\frac{5 θ}{5} : θ

\frac{5 θ}{5}

数を割る:

\frac{5}{5} = 1

= θ

簡素化

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ} : 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 5 \cdot 36 0^{\circ} n - 5 \cdot 2 3^{\circ}

5 \cdot 36 0^{\circ} n = 180 0^{\circ} n

5 \cdot 36 0^{\circ} n

数を乗じる:

5 \cdot 2 = 10

= 180 0^{\circ} n

5 \cdot 2 3^{\circ} = 11 5^{\circ}

5 \cdot 2 3^{\circ}

分数を乗じる:

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

= 11 5^{\circ}

数を乗じる:

23 \cdot 5 = 115

= 11 5^{\circ}

共通因数を約分する:

5

= 11 5^{\circ}

= 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

θ = 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 arccsc (\frac{8 3}{7}) + 180 0^{\circ} n - 11 5^{\circ}

10進法形式で解を証明する

θ = 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}, θ = 90 0^{\circ} - 5 \cdot 0.52959 \dots + 180 0^{\circ} n - 11 5^{\circ}

グラフ

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