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人気のある三角関数 >

sin(x+20)*csc(70)=1

解

sin (x + 2 0^{\circ}) \cdot csc (7 0^{\circ}) = 1

解

x = 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}

+1

ラジアン

x = 1.22173 \dots - \frac{π}{9} + 2 πn, x = π - 1.22173 \dots - \frac{π}{9} + 2 πn

解答ステップ

sin (x + 2 0^{\circ}) csc (7 0^{\circ}) = 1

以下で両辺を割る

csc (7 0^{\circ})

sin (x + 2 0^{\circ}) csc (7 0^{\circ}) = 1

以下で両辺を割る

csc (7 0^{\circ})

\frac{sin ( x + 2 0 ^{\circ} ) csc ( 7 0 ^{\circ} )}{csc ( 7 0 ^{\circ} )} = \frac{1}{csc ( 7 0 ^{\circ} )}

簡素化

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

三角関数の逆数プロパティを適用する

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

以下の一般解

sin (x + 2 0^{\circ}) = \frac{1}{csc ( 7 0 ^{\circ} )}

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

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n, x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

解く

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n : x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

2 0^{\circ}

を右側に移動します

x + 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

両辺から

2 0^{\circ}

を引く

x + 2 0^{\circ} - 2 0^{\circ} = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

簡素化

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

解く

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

2 0^{\circ}

を右側に移動します

x + 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n

両辺から

2 0^{\circ}

を引く

x + 2 0^{\circ} - 2 0^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

簡素化

x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

x = arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{csc ( 7 0 ^{\circ} )}) + 36 0^{\circ} n - 2 0^{\circ}

10進法形式で解を証明する

x = 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}, x = 18 0^{\circ} - 1.22173 \dots + 36 0^{\circ} n - 2 0^{\circ}

グラフ

人気の例

sec^{2} (t) = 0

solvefor x,t=tan(x/2)

so l v e f or x, t = tan (\frac{x}{2})

sin^2(x)=8cos^2(x)

sin^{2} (x) = 8 cos^{2} (x)

sin(x)+cos(x)=0,0<= x<= 360

sin (x) + cos (x) = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

sin (θ) = - 0.342