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人気のある三角関数 >

sin(2x)= 3/5

解

sin (2 x) = \frac{3}{5}

解

x = \frac{0.64350 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.64350 \dots}{2} + πn

+1

度

x = 18.43494 \dots^{\circ} + 18 0^{\circ} n, x = 71.56505 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

sin (2 x) = \frac{3}{5}

三角関数の逆数プロパティを適用する

sin (2 x) = \frac{3}{5}

以下の一般解

sin (2 x) = \frac{3}{5}

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

2 x = arcsin (\frac{3}{5}) + 2 πn, 2 x = π - arcsin (\frac{3}{5}) + 2 πn

2 x = arcsin (\frac{3}{5}) + 2 πn, 2 x = π - arcsin (\frac{3}{5}) + 2 πn

解く

2 x = arcsin (\frac{3}{5}) + 2 πn : x = \frac{arcsin ( \frac{3}{5} )}{2} + πn

2 x = arcsin (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

2 x = arcsin (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{arcsin ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

簡素化

x = \frac{arcsin ( \frac{3}{5} )}{2} + πn

x = \frac{arcsin ( \frac{3}{5} )}{2} + πn

解く

2 x = π - arcsin (\frac{3}{5}) + 2 πn : x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

2 x = π - arcsin (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

2 x = π - arcsin (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

\frac{2 x}{2} = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

簡素化

x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

x = \frac{arcsin ( \frac{3}{5} )}{2} + πn, x = \frac{π}{2} - \frac{arcsin ( \frac{3}{5} )}{2} + πn

10進法形式で解を証明する

x = \frac{0.64350 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.64350 \dots}{2} + πn

グラフ

人気の例

- cos (x) = sin (x)

2cos^2(x)+5cos(x)-3=0

2 cos^{2} (x) + 5 cos (x) - 3 = 0

solvefor x,cos(x)=1

so l v e f or x, cos (x) = 1

cos(x)cot^2(x)=cos(x)

cos (x) cot^{2} (x) = cos (x)

4sin(x)cos(x)=-9cos(x)

4 sin (x) cos (x) = - 9 cos (x)