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人気のある三角関数 >

sin(135)+cos(135)+tan(135)

解

sin (13 5^{\circ}) + cos (13 5^{\circ}) + tan (13 5^{\circ})

解

- 1

解答ステップ

sin (13 5^{\circ}) + cos (13 5^{\circ}) + tan (13 5^{\circ})

三角関数の公式を使用して書き換える:

tan (13 5^{\circ}) = \frac{sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

tan (13 5^{\circ})

基本的な三角関数の公式を使用する:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

= sin (13 5^{\circ}) + cos (13 5^{\circ}) + \frac{sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

簡素化

= \frac{sin ( 13 5 ^{\circ} ) cos ( 13 5 ^{\circ} ) + cos ^{2} ( 13 5 ^{\circ} ) + sin ( 13 5 ^{\circ} )}{cos ( 13 5 ^{\circ} )}

次の自明恒等式を使用する:

sin (13 5^{\circ}) = \frac{2}{2}

sin (13 5^{\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{2}{2}

次の自明恒等式を使用する:

cos (13 5^{\circ}) = - \frac{2}{2}

cos (13 5^{\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{2}{2}

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

簡素化

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

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

括弧を削除する:

(- a) = - a

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

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

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

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

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

分数の規則を適用する:

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

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

分数の規則を適用する:

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

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

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

累乗根の規則を適用する:

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

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

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

指数の規則を適用する:

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

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

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

数を引く:

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

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

累乗根の規則を適用する:

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

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

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

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

\frac{2}{2} \cdot \frac{2}{2}

分数を乗じる:

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

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

22 = 2

22

累乗根の規則を適用する:

a a = a

22 = 2

= 2

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

数を乗じる:

2 \cdot 2 = 4

= \frac{2}{4}

共通因数を約分する:

2

= \frac{1}{2}

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

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

指数の規則を適用する:

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

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

(2)^{2} : 2

累乗根の規則を適用する:

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

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

指数の規則を適用する:

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

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

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

\frac{1}{2} \cdot 2

分数を乗じる:

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

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

共通因数を約分する:

2

= 1

= 2

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

共通因数を約分する:

2

= \frac{1}{2}

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

分数を組み合わせる

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

規則を適用

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

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

- 1 + 1 = 0

= \frac{2}{2}

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

括弧を削除する:

(a) = a

= - \frac{2}{2} 2

分数を乗じる:

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

= - \frac{2 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}

規則を適用

\frac{a}{a} = 1

= - 1

= - 1

人気の例

tan(arcsin((-12)/(13)))

tan (arcsin (\frac{- 12}{13}))

sec(arccos(-3/5))

sec (arccos (- \frac{3}{5}))

6 sin (1 0^{\circ})

(cos(pi/4)+isin(pi/4))^{100}

(cos (\frac{π}{4}) + i sin (\frac{π}{4}))^{100}

sin (6 \frac{π}{9})