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人気のある三角関数 >

cos(2B)= 21/35

解

cos (2 B) = \frac{21}{35}

解

B = \frac{0.92729 \dots}{2} + πn, B = π - \frac{0.92729 \dots}{2} + πn

+1

度

B = 26.56505 \dots^{\circ} + 18 0^{\circ} n, B = 153.43494 \dots^{\circ} + 18 0^{\circ} n

解答ステップ

cos (2 B) = \frac{21}{35}

共通因数を約分する:

7

cos (2 B) = \frac{3}{5}

三角関数の逆数プロパティを適用する

cos (2 B) = \frac{3}{5}

以下の一般解

cos (2 B) = \frac{3}{5}

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

2 B = arccos (\frac{3}{5}) + 2 πn, 2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

2 B = arccos (\frac{3}{5}) + 2 πn, 2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

解く

2 B = arccos (\frac{3}{5}) + 2 πn : B = \frac{arccos ( \frac{3}{5} )}{2} + πn

2 B = arccos (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

2 B = arccos (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

\frac{2 B}{2} = \frac{arccos ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

簡素化

B = \frac{arccos ( \frac{3}{5} )}{2} + πn

B = \frac{arccos ( \frac{3}{5} )}{2} + πn

解く

2 B = 2 π - arccos (\frac{3}{5}) + 2 πn : B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

2 B = 2 π - arccos (\frac{3}{5}) + 2 πn

以下で両辺を割る

2

\frac{2 B}{2} = \frac{2 π}{2} - \frac{arccos ( \frac{3}{5} )}{2} + \frac{2 πn}{2}

簡素化

B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

B = \frac{arccos ( \frac{3}{5} )}{2} + πn, B = π - \frac{arccos ( \frac{3}{5} )}{2} + πn

10進法形式で解を証明する

B = \frac{0.92729 \dots}{2} + πn, B = π - \frac{0.92729 \dots}{2} + πn

グラフ

人気の例

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sin^{2} (x) = cos (x) - cos^{2} (x)

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sin(x-15)=cos(20+x)

sin (x - 1 5^{\circ}) = cos (2 0^{\circ} + x)

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15 sin^{2} (x) - 17 sin (x) + 4 = 0

tan^2(x)=2sec(x)

tan^{2} (x) = 2 sec (x)