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人気のある三角関数 >

((30)^2sin^2(30))/(2*9.81^2)

解

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

解

\frac{125000}{106929}

+1

十進法表記

1.16899 \dots

解答ステップ

\frac{( 30 ) ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 \cdot 9.8 1 ^{2}}

= \frac{3 0 ^{2} sin ^{2} ( 3 0 ^{\circ} )}{2 ( \frac{981}{100} ) ^{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}

= \frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

簡素化

\frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}} : \frac{125000}{106929}

\frac{3 0 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

因数

3 0^{2} : 2^{2} \cdot 3^{2} \cdot 5^{2}

因数

30 = 2 \cdot 3 \cdot 5

= (2 \cdot 3 \cdot 5)^{2}

指数の規則を適用する:

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

= 2^{2} \cdot 3^{2} \cdot 5^{2}

= \frac{2 ^{2} \cdot 3 ^{2} \cdot 5 ^{2} ( \frac{1}{2} ) ^{2}}{2 ( \frac{981}{100} ) ^{2}}

共通因数を約分する:

2

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 ( \frac{1}{2} ) ^{2}}{( \frac{981}{100} ) ^{2}}

(\frac{981}{100})^{2} = \frac{98 1 ^{2}}{10 0 ^{2}}

(\frac{981}{100})^{2}

指数の規則を適用する:

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

= \frac{98 1 ^{2}}{10 0 ^{2}}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 ( \frac{1}{2} ) ^{2}}{\frac{98 1 ^{2}}{10 0 ^{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}}

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}}{\frac{98 1 ^{2}}{10 0 ^{2}}}

分数の規則を適用する:

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

= \frac{3 ^{2} \cdot 5 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0 ^{2}}{98 1 ^{2}}

簡素化

3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0^{2} : 5^{6} \cdot 3^{2} \cdot 4^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}

3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 10 0^{2}

整数を因数分解する

100 = 5^{2} \cdot 4

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} (5^{2} \cdot 4)^{2}

指数の規則を適用する:

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

(5^{2} \cdot 4)^{2} = (5^{2})^{2} \cdot 4^{2}

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} (5^{2})^{2} \cdot 4^{2}

指数の規則を適用する:

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

(5^{2})^{2} = 5^{2 \cdot 2}

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{2 \cdot 2} \cdot 4^{2}

改良

= 3^{2} \cdot 5^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{4} \cdot 4^{2}

指数の規則を適用する:

a^{b} \cdot a^{c} = a^{b + c}

5^{2} \cdot 5^{4} = 5^{2 + 4}

= 3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{2 + 4} \cdot 4^{2}

数を足す:

2 + 4 = 6

= 3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2} \cdot 2 \cdot \frac{1}{2 ^{2}}}{98 1 ^{2}}

乗じる

3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2} : 1125000

3^{2} \cdot 2 \cdot \frac{1}{2 ^{2}} \cdot 5^{6} \cdot 4^{2}

分数を乗じる:

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

= \frac{1 \cdot 3 ^{2} \cdot 2 \cdot 5 ^{6} \cdot 4 ^{2}}{2 ^{2}}

数を乗じる:

1 \cdot 2 = 2

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2} \cdot 2}{2 ^{2}}

共通因数を約分する:

2

= \frac{5 ^{6} \cdot 3 ^{2} \cdot 4 ^{2}}{2}

因数

4^{2} : 2^{4}

因数

4 = 2^{2}

= (2^{2})^{2}

簡素化

(2^{2})^{2} : 2^{4}

(2^{2})^{2}

指数の規則を適用する:

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

= 2^{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= 2^{4}

= 2^{4}

= \frac{5 ^{6} \cdot 2 ^{4} \cdot 3 ^{2}}{2}

共通因数を約分する:

2

= 5^{6} \cdot 2^{3} \cdot 3^{2}

5^{6} = 15625

= 2^{3} \cdot 3^{2} \cdot 15625

2^{3} = 8

= 3^{2} \cdot 15625 \cdot 8

3^{2} = 9

= 15625 \cdot 8 \cdot 9

数を乗じる:

15625 \cdot 8 \cdot 9 = 1125000

= 1125000

= \frac{1125000}{98 1 ^{2}}

因数

1125000 : 5^{6} \cdot 2^{3} \cdot 3^{2}

因数

1125000 = 5^{6} \cdot 2^{3} \cdot 3^{2}

因数

98 1^{2} : 3^{4} \cdot 10 9^{2}

因数

981 = 3^{2} \cdot 109

= (3^{2} \cdot 109)^{2}

指数の規則を適用する:

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

= 10 9^{2} (3^{2})^{2}

簡素化

(3^{2})^{2} : 3^{4}

(3^{2})^{2}

指数の規則を適用する:

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

= 3^{2 \cdot 2}

数を乗じる:

2 \cdot 2 = 4

= 3^{4}

= 3^{4} \cdot 10 9^{2}

= \frac{5 ^{6} \cdot 2 ^{3} \cdot 3 ^{2}}{3 ^{4} \cdot 10 9 ^{2}}

キャンセル

\frac{2 ^{3} \cdot 3 ^{2} \cdot 5 ^{6}}{3 ^{4} \cdot 10 9 ^{2}} : \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

\frac{2 ^{3} \cdot 3 ^{2} \cdot 5 ^{6}}{3 ^{4} \cdot 10 9 ^{2}}

指数の規則を適用する:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{3 ^{2}}{3 ^{4}} = \frac{1}{3 ^{4 - 2}}

= \frac{5 ^{6} \cdot 2 ^{3}}{10 9 ^{2} \cdot 3 ^{4 - 2}}

数を引く:

4 - 2 = 2

= \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

= \frac{5 ^{6} \cdot 2 ^{3}}{3 ^{2} \cdot 10 9 ^{2}}

5^{6} \cdot 2^{3} = 125000

5^{6} \cdot 2^{3}

5^{6} = 15625

= 2^{3} \cdot 15625

2^{3} = 8

= 15625 \cdot 8

数を乗じる:

15625 \cdot 8 = 125000

= 125000

= \frac{125000}{3 ^{2} \cdot 10 9 ^{2}}

3^{2} \cdot 10 9^{2} = 106929

3^{2} \cdot 10 9^{2}

3^{2} = 9

= 10 9^{2} \cdot 9

10 9^{2} = 11881

= 9 \cdot 11881

数を乗じる:

9 \cdot 11881 = 106929

= 106929

= \frac{125000}{106929}

= \frac{125000}{106929}

人気の例

tan (4 1^{\circ}) \cdot 3

(5.78)/(tan(38))

\frac{5.78}{tan ( 3 8 ^{\circ} )}

cos^1((sqrt(3))/2)

cos^{1} (\frac{3}{2})

11 \cdot sin (6 5^{\circ})

tan(60)+csc(60)

tan (6 0^{\circ}) + csc (6 0^{\circ})