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人気のある三角関数 >

cos(2θ)= 3/5 ,90<= θ<= 180

解

cos (2 θ) = \frac{3}{5}, 9 0^{\circ} \leq θ \leq 18 0^{\circ}

解

θ = \frac{36 0 ^{\circ} - 0.92729 \dots}{2}

+1

ラジアン

θ = \frac{2 π - 0.92729 \dots}{2}

解答ステップ

cos (2 θ) = \frac{3}{5}, 9 0^{\circ} \leq θ \leq 18 0^{\circ}

三角関数の逆数プロパティを適用する

cos (2 θ) = \frac{3}{5}

以下の一般解

cos (2 θ) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 36 0^{\circ} n, x = 36 0^{\circ} - arccos (a) + 36 0^{\circ} n

2 θ = arccos (\frac{3}{5}) + 36 0^{\circ} n, 2 θ = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

2 θ = arccos (\frac{3}{5}) + 36 0^{\circ} n, 2 θ = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

解く

2 θ = arccos (\frac{3}{5}) + 36 0^{\circ} n : θ = \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

2 θ = arccos (\frac{3}{5}) + 36 0^{\circ} n

以下で両辺を割る

2

2 θ = arccos (\frac{3}{5}) + 36 0^{\circ} n

以下で両辺を割る

2

\frac{2 θ}{2} = \frac{arccos ( \frac{3}{5} )}{2} + \frac{36 0 ^{\circ} n}{2}

簡素化

θ = \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

θ = \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

解く

2 θ = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n : θ = 18 0^{\circ} - \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

2 θ = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

以下で両辺を割る

2

2 θ = 36 0^{\circ} - arccos (\frac{3}{5}) + 36 0^{\circ} n

以下で両辺を割る

2

\frac{2 θ}{2} = 18 0^{\circ} - \frac{arccos ( \frac{3}{5} )}{2} + \frac{36 0 ^{\circ} n}{2}

簡素化

θ = 18 0^{\circ} - \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

θ = 18 0^{\circ} - \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

θ = \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n, θ = 18 0^{\circ} - \frac{arccos ( \frac{3}{5} )}{2} + 18 0^{\circ} n

範囲の解答

9 0^{\circ} \leq θ \leq 18 0^{\circ}

θ = \frac{36 0 ^{\circ} - arccos ( \frac{3}{5} )}{2}

10進法形式で解を証明する

θ = \frac{36 0 ^{\circ} - 0.92729 \dots}{2}

グラフ

人気の例

sin^2(x)-4cos(x)-4=0,0<= x<= 2pi

sin^{2} (x) - 4 cos (x) - 4 = 0, 0 \leq x \leq 2 π

solvefor x,sin(x)=0.5

so l v e f or x, sin (x) = 0.5

solvefor x,z=arcsin(y/x)

so l v e f or x, z = arcsin (\frac{y}{x})

3 csc (A) - 6 = 0

15cos^2(x)+sin(x)-9=0

15 cos^{2} (x) + sin (x) - 9 = 0