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人気のある三角関数 >

(sin(150)+sin(30))/(cos(120)+cos(240))

解

\frac{sin ( 15 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{cos ( 12 0 ^{\circ} ) + cos ( 24 0 ^{\circ} )}

解

- 1

解答ステップ

\frac{sin ( 15 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{cos ( 12 0 ^{\circ} ) + cos ( 24 0 ^{\circ} )}

三角関数の公式を使用して書き換える:

cos (24 0^{\circ}) = 2 cos^{2} (12 0^{\circ}) - 1

cos (24 0^{\circ})

cos (24 0^{\circ})

を以下として書く:

cos (2 \cdot 12 0^{\circ})

= cos (2 \cdot 12 0^{\circ})

2倍角の公式を使用:

cos (2 x) = 2 cos^{2} (x) - 1

= 2 cos^{2} (12 0^{\circ}) - 1

= \frac{sin ( 15 0 ^{\circ} ) + sin ( 3 0 ^{\circ} )}{cos ( 12 0 ^{\circ} ) + 2 cos ^{2} ( 12 0 ^{\circ} ) - 1}

次の自明恒等式を使用する:

sin (15 0^{\circ}) = \frac{1}{2}

sin (15 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}

= \frac{1}{2}

次の自明恒等式を使用する:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 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}

= \frac{1}{2}

次の自明恒等式を使用する:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 0^{\circ})

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{1}{2}

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

簡素化

\frac{\frac{1}{2} + \frac{1}{2}}{- \frac{1}{2} + 2 ( - \frac{1}{2} ) ^{2} - 1} : - 1

\frac{\frac{1}{2} + \frac{1}{2}}{- \frac{1}{2} + 2 ( - \frac{1}{2} ) ^{2} - 1}

分数を組み合わせる

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

規則を適用

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

= \frac{1 + 1}{2}

数を足す:

1 + 1 = 2

= \frac{2}{2}

規則を適用

\frac{a}{a} = 1

= 1

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

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

- \frac{1}{2} + 2 (- \frac{1}{2})^{2} - 1

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

(- \frac{1}{2})^{2}

指数の規則を適用する:

n

が偶数であれば

(- a)^{n} = a^{n}

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

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

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

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

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

2 (\frac{1}{2})^{2}

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

(\frac{1}{2})^{2}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

規則を適用

1^{a} = 1

1^{2} = 1

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

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

分数を乗じる:

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

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

数を乗じる:

1 \cdot 2 = 2

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

共通因数を約分する:

2

= \frac{1}{2}

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

類似した元を足す:

- \frac{1}{2} + \frac{1}{2} = 0

= \frac{1}{- 1}

分数の規則を適用する:

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

= - \frac{1}{1}

規則を適用

\frac{a}{1} = a

= - 1

= - 1

人気の例

-6sin(30)+2cos(60)

- 6 sin (3 0^{\circ}) + 2 cos (6 0^{\circ})

arcsin((9.2)/(15.6))

arcsin (\frac{9.2}{15.6})

arccos (0.371)

arccos(sin(-(11pi)/4))

arccos (sin (- \frac{11 π}{4}))

arcsech (0)