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人気のある三角関数 >

sqrt(11)sin(x+37.09)=1

解

11 sin (x + 37.0 9^{\circ}) = 1

解

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

+1

ラジアン

x = 0.30627 \dots - \frac{245 π}{1189} + 2 πn, x = π - 0.30627 \dots - \frac{245 π}{1189} + 2 πn

解答ステップ

11 sin (x + 37.0 9^{\circ}) = 1

以下で両辺を割る

11

11 sin (x + 37.08999 \dots^{\circ}) = 1

以下で両辺を割る

11

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

簡素化

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} = \frac{1}{11}

簡素化

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11} : sin (x + 37.08999 \dots^{\circ})

\frac{11 sin ( x + 37.08999 \dots ^{\circ} )}{11}

共通因数を約分する:

11

= sin (x + 37.08999 \dots^{\circ})

簡素化

\frac{1}{11} : \frac{11}{11}

\frac{1}{11}

共役で乗じる

\frac{11}{11}

= \frac{1 \cdot 11}{11 11}

1 \cdot 11 = 11

1111 = 11

1111

累乗根の規則を適用する:

a a = a

1111 = 11

= 11

= \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

三角関数の逆数プロパティを適用する

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

以下の一般解

sin (x + 37.08999 \dots^{\circ}) = \frac{11}{11}

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

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n, x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

解く

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n : x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = arcsin (\frac{11}{11}) + 36 0^{\circ} n

簡素化

arcsin (\frac{11}{11}) + 36 0^{\circ} n : arcsin (\frac{1}{11}) + 36 0^{\circ} n

arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{1 1 ^{\frac{1}{2}}}{1 1 ^{1}} = \frac{1}{1 1 ^{1 - \frac{1}{2}}}

= \frac{1}{1 1 ^{1 - \frac{1}{2}}}

数を引く:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{1 1 ^{\frac{1}{2}}}

累乗根の規則を適用する:

a^{\frac{1}{n}} = n a

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

37.08999 \dots^{\circ}

を右側に移動します

x + 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n

両辺から

37.08999 \dots^{\circ}

を引く

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

簡素化

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

解く

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n : x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

簡素化

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n : 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

18 0^{\circ} - arcsin (\frac{11}{11}) + 36 0^{\circ} n

\frac{11}{11} = \frac{1}{11}

\frac{11}{11}

累乗根の規則を適用する:

n a = a^{\frac{1}{n}}

11 = 1 1^{\frac{1}{2}}

= \frac{1 1 ^{\frac{1}{2}}}{11}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{1 1 ^{\frac{1}{2}}}{1 1 ^{1}} = \frac{1}{1 1 ^{1 - \frac{1}{2}}}

= \frac{1}{1 1 ^{1 - \frac{1}{2}}}

数を引く:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{1}{1 1 ^{\frac{1}{2}}}

累乗根の規則を適用する:

a^{\frac{1}{n}} = n a

1 1^{\frac{1}{2}} = 11

= \frac{1}{11}

= 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

37.08999 \dots^{\circ}

を右側に移動します

x + 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n

両辺から

37.08999 \dots^{\circ}

を引く

x + 37.08999 \dots^{\circ} - 37.08999 \dots^{\circ} = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

簡素化

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

x = arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - arcsin (\frac{1}{11}) + 36 0^{\circ} n - 37.08999 \dots^{\circ}

10進法形式で解を証明する

x = 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}, x = 18 0^{\circ} - 0.30627 \dots + 36 0^{\circ} n - 37.08999 \dots^{\circ}

グラフ

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