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人気のある三角関数 >

sin(x/2)= 3/5

解

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

解

x = 2 \cdot 0.64350 \dots + 4 πn, x = 2 π - 2 \cdot 0.64350 \dots + 4 πn

+1

度

x = 73.73979 \dots^{\circ} + 72 0^{\circ} n, x = 286.26020 \dots^{\circ} + 72 0^{\circ} n

解答ステップ

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

三角関数の逆数プロパティを適用する

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

以下の一般解

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

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

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

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

解く

\frac{x}{2} = arcsin (\frac{3}{5}) + 2 πn : x = 2 arcsin (\frac{3}{5}) + 4 πn

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

以下で両辺を乗じる:

2

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

以下で両辺を乗じる:

2

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

簡素化

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

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn : 2 arcsin (\frac{3}{5}) + 4 πn

2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn

数を乗じる:

2 \cdot 2 = 4

= 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn

解く

\frac{x}{2} = π - arcsin (\frac{3}{5}) + 2 πn : x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

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

以下で両辺を乗じる:

2

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

以下で両辺を乗じる:

2

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

簡素化

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

簡素化

\frac{2 x}{2} : x

\frac{2 x}{2}

数を割る:

\frac{2}{2} = 1

= x

簡素化

2 π - 2 arcsin (\frac{3}{5}) + 2 \cdot 2 πn : 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

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

数を乗じる:

2 \cdot 2 = 4

= 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

x = 2 arcsin (\frac{3}{5}) + 4 πn, x = 2 π - 2 arcsin (\frac{3}{5}) + 4 πn

10進法形式で解を証明する

x = 2 \cdot 0.64350 \dots + 4 πn, x = 2 π - 2 \cdot 0.64350 \dots + 4 πn

グラフ

人気の例

16 cos^{2} (x) - 8 = 0

2 sin (4 θ) = 0

solvefor θ,4sin^2(θ/2)+8cos(θ/2)-7=0

so l v e f or θ, 4 sin^{2} (\frac{θ}{2}) + 8 cos (\frac{θ}{2}) - 7 = 0

2sin^2(x)-sin(x)=0,0<= x<= 2pi

2 sin^{2} (x) - sin (x) = 0, 0 \leq x \leq 2 π

tan(x)=(sqrt(2))/2

tan (x) = \frac{2}{2}