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人気のある三角関数 >

sin(5x-1)= 4/5

解

sin (5 x - 1) = \frac{4}{5}

解

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

+1

度

x = 22.08517 \dots^{\circ} + 7 2^{\circ} n, x = 36.83313 \dots^{\circ} + 7 2^{\circ} n

解答ステップ

sin (5 x - 1) = \frac{4}{5}

三角関数の逆数プロパティを適用する

sin (5 x - 1) = \frac{4}{5}

以下の一般解

sin (5 x - 1) = \frac{4}{5}

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn, 5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

解く

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn : x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

1

を右側に移動します

5 x - 1 = arcsin (\frac{4}{5}) + 2 πn

両辺に

1

を足す

5 x - 1 + 1 = arcsin (\frac{4}{5}) + 2 πn + 1

簡素化

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

以下で両辺を割る

5

5 x = arcsin (\frac{4}{5}) + 2 πn + 1

以下で両辺を割る

5

\frac{5 x}{5} = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

簡素化

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

解く

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn : x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

1

を右側に移動します

5 x - 1 = π - arcsin (\frac{4}{5}) + 2 πn

両辺に

1

を足す

5 x - 1 + 1 = π - arcsin (\frac{4}{5}) + 2 πn + 1

簡素化

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

以下で両辺を割る

5

5 x = π - arcsin (\frac{4}{5}) + 2 πn + 1

以下で両辺を割る

5

\frac{5 x}{5} = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

簡素化

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

x = \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{arcsin ( \frac{4}{5} )}{5} + \frac{2 πn}{5} + \frac{1}{5}

10進法形式で解を証明する

x = \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}, x = \frac{π}{5} - \frac{0.92729 \dots}{5} + \frac{2 πn}{5} + \frac{1}{5}

グラフ

人気の例

sin^{2} (x) = \frac{1}{36}

tan (x) = 31

sin^4(x)+cos^2(x)=2

sin^{4} (x) + cos^{2} (x) = 2

5tan(x)=15cot(x)

5 tan (x) = 15 cot (x)

solvefor x,arctan(x)=arctan(y)

so l v e f or x, arctan (x) = arctan (y)