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人気のある三角関数 >

sin(2x)= 1/4

解

sin (2 x) = \frac{1}{4}

解

x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

+1

度

x = 7.23875 \dots^{\circ} + 18 0^{\circ} n, x = 82.76124 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

sin (2 x) = \frac{1}{4}

三角関数の逆数プロパティを適用する

sin (2 x) = \frac{1}{4}

以下の一般解

sin (2 x) = \frac{1}{4}

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

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

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

解く

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

2 x = arcsin (\frac{1}{4}) + 2 πn

以下で両辺を割る

2

2 x = arcsin (\frac{1}{4}) + 2 πn

以下で両辺を割る

2

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

簡素化

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

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

解く

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

2 x = π - arcsin (\frac{1}{4}) + 2 πn

以下で両辺を割る

2

2 x = π - arcsin (\frac{1}{4}) + 2 πn

以下で両辺を割る

2

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

簡素化

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

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

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

10進法形式で解を証明する

x = \frac{0.25268 \dots}{2} + πn, x = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

グラフ

人気の例

sin^{2} (x) = \frac{1}{8}

2cos^2(x)+sin(2x)=0

2 cos^{2} (x) + sin (2 x) = 0

cosh(4x)=16sinh(x)+1

cosh (4 x) = 16 sinh (x) + 1

cos(θ)=((sqrt(3))/2)

cos (θ) = (\frac{3}{2})

cos(x+(3pi)/4)+cos(x-(3pi)/4)=1

cos (x + \frac{3 π}{4}) + cos (x - \frac{3 π}{4}) = 1