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人気のある三角関数 >

32.09(1+0.0053sin^2(45))

解

32.09 (1 + 0.0053 sin^{2} (4 5^{\circ}))

解

\frac{64350077}{2000000}

+1

十進法表記

32.1750385

解答ステップ

32.09 (1 + 0.0053 sin^{2} (4 5^{\circ}))

= \frac{3209}{100} (1 + \frac{53}{10000} sin^{2} (4 5^{\circ}))

次の自明恒等式を使用する:

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

sin (4 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}

= \frac{3209}{100} 1 + \frac{53}{10000} (\frac{2}{2})^{2}

簡素化

\frac{3209}{100} 1 + \frac{53}{10000} (\frac{2}{2})^{2} : \frac{64350077}{2000000}

\frac{3209}{100} 1 + \frac{53}{10000} (\frac{2}{2})^{2}

\frac{53}{10000} (\frac{2}{2})^{2} = \frac{53}{20000}

\frac{53}{10000} (\frac{2}{2})^{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}

= \frac{1}{2} \cdot \frac{53}{10000}

分数を乗じる:

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

= \frac{53 \cdot 1}{10000 \cdot 2}

数を乗じる:

53 \cdot 1 = 53

= \frac{53}{10000 \cdot 2}

数を乗じる:

10000 \cdot 2 = 20000

= \frac{53}{20000}

= \frac{3209}{100} (\frac{53}{20000} + 1)

結合

1 + \frac{53}{20000} : \frac{20053}{20000}

1 + \frac{53}{20000}

元を分数に変換する:

1 = \frac{1 \cdot 20000}{20000}

= \frac{1 \cdot 20000}{20000} + \frac{53}{20000}

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 20000 + 53}{20000}

1 \cdot 20000 + 53 = 20053

1 \cdot 20000 + 53

数を乗じる:

1 \cdot 20000 = 20000

= 20000 + 53

数を足す:

20000 + 53 = 20053

= 20053

= \frac{20053}{20000}

= \frac{3209}{100} \cdot \frac{20053}{20000}

分数を乗じる:

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

= \frac{3209 \cdot 20053}{100 \cdot 20000}

数を乗じる:

3209 \cdot 20053 = 64350077

= \frac{64350077}{100 \cdot 20000}

数を乗じる:

100 \cdot 20000 = 2000000

= \frac{64350077}{2000000}

= \frac{64350077}{2000000}

人気の例

arctan(tan(-pi/7))

arctan (tan (- \frac{π}{7}))

arctan((6.1)/4)

arctan (\frac{6.1}{4})

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