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人気のある三角関数 >

(((1-sin^2(x)))/((1+2*sin^2(x))))=0.45

解

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 \cdot sin ^{2} ( x ) )}) = 0.45

解

x = 0.56809 \dots + 2 πn, x = π - 0.56809 \dots + 2 πn, x = - 0.56809 \dots + 2 πn, x = π + 0.56809 \dots + 2 πn

+1

度

x = 32.54946 \dots^{\circ} + 36 0^{\circ} n, x = 147.45053 \dots^{\circ} + 36 0^{\circ} n, x = - 32.54946 \dots^{\circ} + 36 0^{\circ} n, x = 212.54946 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 sin ^{2} ( x ) )}) = 0.45

置換で解く

\frac{1 - sin ^{2} ( x )}{1 + 2 sin ^{2} ( x )} = 0.45

仮定:

sin (x) = u

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45 : u = \frac{11}{38}, u = - \frac{11}{38}

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45

以下で両辺を乗じる:

1 + 2 u^{2}

\frac{1 - u ^{2}}{1 + 2 u ^{2}} = 0.45

以下で両辺を乗じる:

1 + 2 u^{2}

\frac{1 - u ^{2}}{1 + 2 u ^{2}} (1 + 2 u^{2}) = 0.45 (1 + 2 u^{2})

簡素化

1 - u^{2} = 0.45 (1 + 2 u^{2})

1 - u^{2} = 0.45 (1 + 2 u^{2})

解く

1 - u^{2} = 0.45 (1 + 2 u^{2}) : u = \frac{11}{38}, u = - \frac{11}{38}

1 - u^{2} = 0.45 (1 + 2 u^{2})

拡張

0.45 (1 + 2 u^{2}) : 0.45 + 0.9 u^{2}

0.45 (1 + 2 u^{2})

分配法則を適用する:

a (b + c) = ab + a c

a = 0.45, b = 1, c = 2 u^{2}

= 0.45 \cdot 1 + 0.45 \cdot 2 u^{2}

= 1 \cdot 0.45 + 2 \cdot 0.45 u^{2}

簡素化

1 \cdot 0.45 + 2 \cdot 0.45 u^{2} : 0.45 + 0.9 u^{2}

1 \cdot 0.45 + 2 \cdot 0.45 u^{2}

数を乗じる:

1 \cdot 0.45 = 0.45

= 0.45 + 2 \cdot 0.45 u^{2}

数を乗じる:

2 \cdot 0.45 = 0.9

= 0.45 + 0.9 u^{2}

= 0.45 + 0.9 u^{2}

1 - u^{2} = 0.45 + 0.9 u^{2}

1

を右側に移動します

1 - u^{2} = 0.45 + 0.9 u^{2}

両辺から

1

を引く

1 - u^{2} - 1 = 0.45 + 0.9 u^{2} - 1

簡素化

- u^{2} = 0.9 u^{2} - 0.55

- u^{2} = 0.9 u^{2} - 0.55

0.9 u^{2}

を左側に移動します

- u^{2} = 0.9 u^{2} - 0.55

両辺から

0.9 u^{2}

を引く

- u^{2} - 0.9 u^{2} = 0.9 u^{2} - 0.55 - 0.9 u^{2}

簡素化

- 1.9 u^{2} = - 0.55

- 1.9 u^{2} = - 0.55

以下で両辺を乗じる:

100

- 1.9 u^{2} = - 0.55

小数点を取り除くには, 小数点以下の各桁に10を乗じます小数点の右側は

2

桁なので,

100 を乗じます

- 1.9 u^{2} \cdot 100 = - 0.55 \cdot 100

改良

- 190 u^{2} = - 55

- 190 u^{2} = - 55

以下で両辺を割る

- 190

- 190 u^{2} = - 55

以下で両辺を割る

- 190

\frac{- 190 u ^{2}}{- 190} = \frac{- 55}{- 190}

簡素化

\frac{- 190 u ^{2}}{- 190} = \frac{- 55}{- 190}

簡素化

\frac{- 190 u ^{2}}{- 190} : u^{2}

\frac{- 190 u ^{2}}{- 190}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{190 u ^{2}}{190}

数を割る:

\frac{190}{190} = 1

= u^{2}

簡素化

\frac{- 55}{- 190} : \frac{11}{38}

\frac{- 55}{- 190}

分数の規則を適用する:

\frac{- a}{- b} = \frac{a}{b}

= \frac{55}{190}

共通因数を約分する:

5

= \frac{11}{38}

u^{2} = \frac{11}{38}

u^{2} = \frac{11}{38}

u^{2} = \frac{11}{38}

x^{2} = f (a)

の場合, 解は

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

u = \frac{11}{38}, u = - \frac{11}{38}

u = \frac{11}{38}, u = - \frac{11}{38}

代用を戻す

u = sin (x)

sin (x) = \frac{11}{38}, sin (x) = - \frac{11}{38}

sin (x) = \frac{11}{38}, sin (x) = - \frac{11}{38}

sin (x) = \frac{11}{38} : x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn

sin (x) = \frac{11}{38}

三角関数の逆数プロパティを適用する

sin (x) = \frac{11}{38}

以下の一般解

sin (x) = \frac{11}{38}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn

x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn

sin (x) = - \frac{11}{38} : x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

sin (x) = - \frac{11}{38}

三角関数の逆数プロパティを適用する

sin (x) = - \frac{11}{38}

以下の一般解

sin (x) = - \frac{11}{38}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

すべての解を組み合わせる

x = arcsin (\frac{11}{38}) + 2 πn, x = π - arcsin (\frac{11}{38}) + 2 πn, x = arcsin (- \frac{11}{38}) + 2 πn, x = π + arcsin (\frac{11}{38}) + 2 πn

10進法形式で解を証明する

x = 0.56809 \dots + 2 πn, x = π - 0.56809 \dots + 2 πn, x = - 0.56809 \dots + 2 πn, x = π + 0.56809 \dots + 2 πn

グラフ

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