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人気のある三角関数 >

sin(arccos(-1)-arccos(1/2))

解

sin (arccos (- 1) - arccos (\frac{1}{2}))

解

\frac{3}{2}

+1

十進法表記

0.86602 \dots

解答ステップ

sin (arccos (- 1) - arccos (\frac{1}{2}))

三角関数の公式を使用して書き換える:

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

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

和・積の公式を使用する:

arccos (s) - arccos (t) = arccos (s t + (1 - s^{2}) (1 - t^{2}))

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

簡素化:

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

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

括弧を削除する:

(- a) = - a

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

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

1 \cdot \frac{1}{2}

乗算:

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

= \frac{1}{2}

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

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

(- 1)^{2} = 1

(- 1)^{2}

指数の規則を適用する:

n

が偶数であれば

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

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

= 1^{2}

規則を適用

1^{a} = 1

= 1

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

(\frac{1}{2})^{2} = \frac{1}{4}

(\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^{2} = 4

= \frac{1}{4}

= (1 - 1) (- \frac{1}{4} + 1)

数を引く:

1 - 1 = 0

= 0 \cdot (- \frac{1}{4} + 1)

結合

1 - \frac{1}{4} : \frac{3}{4}

1 - \frac{1}{4}

元を分数に変換する:

1 = \frac{1 \cdot 4}{4}

= \frac{1 \cdot 4}{4} - \frac{1}{4}

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{1 \cdot 4 - 1}{4}

1 \cdot 4 - 1 = 3

1 \cdot 4 - 1

数を乗じる:

1 \cdot 4 = 4

= 4 - 1

数を引く:

4 - 1 = 3

= 3

= \frac{3}{4}

= 0 \cdot \frac{3}{4}

規則を適用

0 \cdot a = 0

= 0

規則を適用

0 = 0

= 0

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

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

= - \frac{1}{2}

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

= sin (arccos (- \frac{1}{2}))

三角関数の公式を使用して書き換える:

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

次の恒等式を使用する:

sin (arccos (x)) = 1 - x^{2}

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

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

簡素化

= \frac{3}{2}

人気の例

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