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人気のある三角関数 >

9.6=11.6cos(3.922t)

解

9.6 = 11.6 cos (3.922 t)

解

t = \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}

+1

度

t = 8.70689 \dots^{\circ} + 91.78990 \dots^{\circ} n, t = 83.08301 \dots^{\circ} + 91.78990 \dots^{\circ} n

解答ステップ

9.6 = 11.6 cos (3.922 t)

辺を交換する

11.6 cos (3.922 t) = 9.6

以下で両辺を乗じる:

10

11.6 cos (3.922 t) = 9.6

小数点を取り除くには, 小数点以下の各桁に10を乗じます小数点の右側は1桁なので,

10 を乗じます

11.6 cos (3.922 t) \cdot 10 = 9.6 \cdot 10

改良

116 cos (3.922 t) = 96

116 cos (3.922 t) = 96

以下で両辺を割る

116

116 cos (3.922 t) = 96

以下で両辺を割る

116

\frac{116 cos ( 3.922 t )}{116} = \frac{96}{116}

簡素化

cos (3.922 t) = \frac{24}{29}

cos (3.922 t) = \frac{24}{29}

三角関数の逆数プロパティを適用する

cos (3.922 t) = \frac{24}{29}

以下の一般解

cos (3.922 t) = \frac{24}{29}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

3.922 t = arccos (\frac{24}{29}) + 2 πn, 3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

3.922 t = arccos (\frac{24}{29}) + 2 πn, 3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

解く

3.922 t = arccos (\frac{24}{29}) + 2 πn : t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = arccos (\frac{24}{29}) + 2 πn

以下で両辺を割る

3.922

3.922 t = arccos (\frac{24}{29}) + 2 πn

以下で両辺を割る

3.922

\frac{3.922 t}{3.922} = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

簡素化

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

解く

3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn : t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

以下で両辺を割る

3.922

3.922 t = 2 π - arccos (\frac{24}{29}) + 2 πn

以下で両辺を割る

3.922

\frac{3.922 t}{3.922} = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

簡素化

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

t = \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{arccos ( \frac{24}{29} )}{3.922} + \frac{2 πn}{3.922}

10進法形式で解を証明する

t = \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}, t = \frac{2 π}{3.922} - \frac{0.59600 \dots}{3.922} + \frac{2 πn}{3.922}

グラフ

人気の例

cos (θ) = 0.5632

sin (z) = - 10

cos^{3} (x) = - 1

sin (θ) = \frac{35}{37}

2cos^2(x)-7cos(x)=-3,0<= x<= 2pi

2 cos^{2} (x) - 7 cos (x) = - 3, 0 \leq x \leq 2 π