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人気のある三角関数 >

sin(x)+sin(90-x)=sin(90)

解

sin (x) + sin (9 0^{\circ} - x) = sin (9 0^{\circ})

解

x = 9 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} + 36 0^{\circ} n

+1

ラジアン

x = \frac{π}{2} + 2 πn, x = 2 π + 2 πn

解答ステップ

sin (x) + sin (9 0^{\circ} - x) = sin (9 0^{\circ})

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

次の自明恒等式を使用する:

sin (9 0^{\circ}) = 1

sin (9 0^{\circ})

sin (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 1

= 1

sin (x) + sin (9 0^{\circ} - x) = 1

三角関数の公式を使用して書き換える

sin (x) + sin (9 0^{\circ} - x)

和・積の公式を使用する:

sin (s) + sin (t) = 2 sin (\frac{s + t}{2}) cos (\frac{s - t}{2})

= 2 sin (\frac{x + 9 0 ^{\circ} - x}{2}) cos (\frac{x - ( 9 0 ^{\circ} - x )}{2})

簡素化

2 sin (\frac{x + 9 0 ^{\circ} - x}{2}) cos (\frac{x - ( 9 0 ^{\circ} - x )}{2}) : 2 cos (\frac{4 x - 18 0 ^{\circ}}{4})

2 sin (\frac{x + 9 0 ^{\circ} - x}{2}) cos (\frac{x - ( 9 0 ^{\circ} - x )}{2})

\frac{x + 9 0 ^{\circ} - x}{2} = 4 5^{\circ}

\frac{x + 9 0 ^{\circ} - x}{2}

x + 9 0^{\circ} - x = 9 0^{\circ}

x + 9 0^{\circ} - x

条件のようなグループ

= x - x + 9 0^{\circ}

類似した元を足す:

x - x = 0

= 9 0^{\circ}

= \frac{9 0 ^{\circ}}{2}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= 4 5^{\circ}

= 2 sin (4 5^{\circ}) cos (\frac{x - ( - x + 9 0 ^{\circ} )}{2})

\frac{x - ( 9 0 ^{\circ} - x )}{2} = \frac{4 x - 18 0 ^{\circ}}{4}

\frac{x - ( 9 0 ^{\circ} - x )}{2}

拡張

x - (9 0^{\circ} - x) : 2 x - 9 0^{\circ}

x - (9 0^{\circ} - x)

- (9 0^{\circ} - x) : - 9 0^{\circ} + x

- (9 0^{\circ} - x)

括弧を分配する

= - (9 0^{\circ}) - (- x)

マイナス・プラスの規則を適用する

- (- a) = a, - (a) = - a

= - 9 0^{\circ} + x

= x - 9 0^{\circ} + x

簡素化

x - 9 0^{\circ} + x : 2 x - 9 0^{\circ}

x - 9 0^{\circ} + x

条件のようなグループ

= x + x - 9 0^{\circ}

類似した元を足す:

x + x = 2 x

= 2 x - 9 0^{\circ}

= 2 x - 9 0^{\circ}

= \frac{2 x - 9 0 ^{\circ}}{2}

結合

2 x - 9 0^{\circ} : \frac{4 x - 18 0 ^{\circ}}{2}

2 x - 9 0^{\circ}

元を分数に変換する:

2 x = \frac{2 x 2}{2}

= \frac{2 x \cdot 2}{2} - 9 0^{\circ}

分母が等しいので, 分数を組み合わせる:

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

= \frac{2 x \cdot 2 - 18 0 ^{\circ}}{2}

数を乗じる:

2 \cdot 2 = 4

= \frac{4 x - 18 0 ^{\circ}}{2}

= \frac{\frac{4 x - 18 0 ^{\circ}}{2}}{2}

分数の規則を適用する:

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

= \frac{4 x - 18 0 ^{\circ}}{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= \frac{4 x - 18 0 ^{\circ}}{4}

= 2 sin (4 5^{\circ}) cos (\frac{4 x - 18 0 ^{\circ}}{4})

簡素化

sin (4 5^{\circ}) : \frac{2}{2}

sin (4 5^{\circ})

次の自明恒等式を使用する:

sin (4 5^{\circ}) = \frac{2}{2}

sin (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= 2 \cdot \frac{2}{2} cos (\frac{4 x - 18 0 ^{\circ}}{4})

分数を乗じる:

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

= \frac{2 \cdot 2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2}

共通因数を約分する:

2

= 2 cos (\frac{4 x - 18 0 ^{\circ}}{4})

= 2 cos (\frac{4 x - 18 0 ^{\circ}}{4})

2 cos (\frac{4 x - 18 0 ^{\circ}}{4}) = 1

以下で両辺を割る

2

2 cos (\frac{4 x - 18 0 ^{\circ}}{4}) = 1

以下で両辺を割る

2

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2} = \frac{1}{2}

簡素化

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2} = \frac{1}{2}

簡素化

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2} : cos (\frac{4 x - 18 0 ^{\circ}}{4})

\frac{2 cos ( \frac{4 x - 18 0 ^{\circ}}{4} )}{2}

共通因数を約分する:

2

= cos (\frac{4 x - 18 0 ^{\circ}}{4})

簡素化

\frac{1}{2} : \frac{2}{2}

\frac{1}{2}

共役で乗じる

\frac{2}{2}

= \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

累乗根の規則を適用する:

a a = a

22 = 2

= 2

= \frac{2}{2}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

以下の一般解

cos (\frac{4 x - 18 0 ^{\circ}}{4}) = \frac{2}{2}

cos (x)

36 0^{\circ} n

循環を含む周期性テーブル:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n, \frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n, \frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

解く

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n : x = 9 0^{\circ} + 36 0^{\circ} n

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

4

\frac{4 x - 18 0 ^{\circ}}{4} = 4 5^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

4

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n

簡素化

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n

簡素化

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} : 4 x - 18 0^{\circ}

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4}

数を割る:

\frac{4}{4} = 1

= 4 x - 18 0^{\circ}

簡素化

4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n : 18 0^{\circ} + 144 0^{\circ} n

4 \cdot 4 5^{\circ} + 4 \cdot 36 0^{\circ} n

4 \cdot 4 5^{\circ} = 18 0^{\circ}

4 \cdot 4 5^{\circ}

分数を乗じる:

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

= 18 0^{\circ}

共通因数を約分する:

4

= 18 0^{\circ}

4 \cdot 36 0^{\circ} n = 144 0^{\circ} n

4 \cdot 36 0^{\circ} n

数を乗じる:

4 \cdot 2 = 8

= 144 0^{\circ} n

= 18 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

18 0^{\circ}

を右側に移動します

4 x - 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n

両辺に

18 0^{\circ}

を足す

4 x - 18 0^{\circ} + 18 0^{\circ} = 18 0^{\circ} + 144 0^{\circ} n + 18 0^{\circ}

簡素化

4 x = 36 0^{\circ} + 144 0^{\circ} n

4 x = 36 0^{\circ} + 144 0^{\circ} n

以下で両辺を割る

4

4 x = 36 0^{\circ} + 144 0^{\circ} n

以下で両辺を割る

4

\frac{4 x}{4} = 9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

簡素化

\frac{4 x}{4} = 9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

簡素化

\frac{4 x}{4} : x

\frac{4 x}{4}

数を割る:

\frac{4}{4} = 1

= x

簡素化

9 0^{\circ} + \frac{144 0 ^{\circ} n}{4} : 9 0^{\circ} + 36 0^{\circ} n

9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

キャンセル

9 0^{\circ} : 9 0^{\circ}

9 0^{\circ}

共通因数を約分する:

2

= 9 0^{\circ}

= 9 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

数を割る:

\frac{8}{4} = 2

= 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n

解く

\frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n : x = 36 0^{\circ} + 36 0^{\circ} n

\frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

4

\frac{4 x - 18 0 ^{\circ}}{4} = 31 5^{\circ} + 36 0^{\circ} n

以下で両辺を乗じる:

4

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n

簡素化

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} = 4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n

簡素化

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4} : 4 x - 18 0^{\circ}

\frac{4 ( 4 x - 18 0 ^{\circ} )}{4}

数を割る:

\frac{4}{4} = 1

= 4 x - 18 0^{\circ}

簡素化

4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n : 126 0^{\circ} + 144 0^{\circ} n

4 \cdot 31 5^{\circ} + 4 \cdot 36 0^{\circ} n

4 \cdot 31 5^{\circ} = 126 0^{\circ}

4 \cdot 31 5^{\circ}

分数を乗じる:

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

= 126 0^{\circ}

共通因数を約分する:

4

= 126 0^{\circ}

4 \cdot 36 0^{\circ} n = 144 0^{\circ} n

4 \cdot 36 0^{\circ} n

数を乗じる:

4 \cdot 2 = 8

= 144 0^{\circ} n

= 126 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

18 0^{\circ}

を右側に移動します

4 x - 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n

両辺に

18 0^{\circ}

を足す

4 x - 18 0^{\circ} + 18 0^{\circ} = 126 0^{\circ} + 144 0^{\circ} n + 18 0^{\circ}

簡素化

4 x = 144 0^{\circ} + 144 0^{\circ} n

4 x = 144 0^{\circ} + 144 0^{\circ} n

以下で両辺を割る

4

4 x = 144 0^{\circ} + 144 0^{\circ} n

以下で両辺を割る

4

\frac{4 x}{4} = 36 0^{\circ} + \frac{144 0 ^{\circ} n}{4}

簡素化

x = 36 0^{\circ} + 36 0^{\circ} n

x = 36 0^{\circ} + 36 0^{\circ} n

x = 9 0^{\circ} + 36 0^{\circ} n, x = 36 0^{\circ} + 36 0^{\circ} n

グラフ

人気の例

sin(2x)=cos(x-60)

sin (2 x) = cos (x - 6 0^{\circ})

tan(x)= 1/(cos^2(x))

tan (x) = \frac{1}{cos ^{2} ( x )}

2csc(θ)=sqrt(2)cot(θ)+3csc(θ)

2 csc (θ) = 2 cot (θ) + 3 csc (θ)

arctan (x) = 180

cos(θ)=(2sqrt(2))/3

cos (θ) = \frac{2 2}{3}