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人気のある三角関数 >

1/2 (6.50941)+cos(θ)(10.40478)=12

解

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12

解

θ = 0.57257 \dots + 2 πn, θ = 2 π - 0.57257 \dots + 2 πn

+1

度

θ = 32.80625 \dots^{\circ} + 36 0^{\circ} n, θ = 327.19374 \dots^{\circ} + 36 0^{\circ} n

解答ステップ

\frac{1}{2} (6.50941) + cos (θ) (10.40478) = 12

\frac{1}{2} \cdot 6.50941 = \frac{6.50941}{2}

\frac{1}{2} \cdot 6.50941

分数を乗じる:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 6.50941}{2}

数を乗じる:

1 \cdot 6.50941 = 6.50941

= \frac{6.50941}{2}

\frac{6.50941}{2} + 10.40478 cos (θ) = 12

\frac{6.50941}{2}

を右側に移動します

\frac{6.50941}{2} + 10.40478 cos (θ) = 12

両辺から

\frac{6.50941}{2}

を引く

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2} = 12 - \frac{6.50941}{2}

簡素化

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2} = 12 - \frac{6.50941}{2}

簡素化

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2} : 10.40478 cos (θ)

\frac{6.50941}{2} + 10.40478 cos (θ) - \frac{6.50941}{2}

類似した元を足す:

\frac{6.50941}{2} - \frac{6.50941}{2} = 0

= 10.40478 cos (θ)

簡素化

12 - \frac{6.50941}{2} : \frac{17.49059}{2}

12 - \frac{6.50941}{2}

元を分数に変換する:

12 = \frac{12 \cdot 2}{2}

= \frac{12 \cdot 2}{2} - \frac{6.50941}{2}

分母が等しいので, 分数を組み合わせる:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{12 \cdot 2 - 6.50941}{2}

12 \cdot 2 - 6.50941 = 17.49059

12 \cdot 2 - 6.50941

数を乗じる:

12 \cdot 2 = 24

= 24 - 6.50941

数を引く:

24 - 6.50941 = 17.49059

= 17.49059

= \frac{17.49059}{2}

10.40478 cos (θ) = \frac{17.49059}{2}

10.40478 cos (θ) = \frac{17.49059}{2}

10.40478 cos (θ) = \frac{17.49059}{2}

以下で両辺を割る

10.40478

10.40478 cos (θ) = \frac{17.49059}{2}

以下で両辺を割る

10.40478

\frac{10.40478 cos ( θ )}{10.40478} = \frac{\frac{17.49059}{2}}{10.40478}

簡素化

\frac{10.40478 cos ( θ )}{10.40478} = \frac{\frac{17.49059}{2}}{10.40478}

簡素化

\frac{10.40478 cos ( θ )}{10.40478} : cos (θ)

\frac{10.40478 cos ( θ )}{10.40478}

共通因数を約分する:

10.40478

= cos (θ)

簡素化

\frac{\frac{17.49059}{2}}{10.40478} : \frac{17.49059}{20.80956}

\frac{\frac{17.49059}{2}}{10.40478}

分数の規則を適用する:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{17.49059}{2 \cdot 10.40478}

数を乗じる:

2 \cdot 10.40478 = 20.80956

= \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

cos (θ) = \frac{17.49059}{20.80956}

三角関数の逆数プロパティを適用する

cos (θ) = \frac{17.49059}{20.80956}

以下の一般解

cos (θ) = \frac{17.49059}{20.80956}

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

θ = arccos (\frac{17.49059}{20.80956}) + 2 πn, θ = 2 π - arccos (\frac{17.49059}{20.80956}) + 2 πn

θ = arccos (\frac{17.49059}{20.80956}) + 2 πn, θ = 2 π - arccos (\frac{17.49059}{20.80956}) + 2 πn

10進法形式で解を証明する

θ = 0.57257 \dots + 2 πn, θ = 2 π - 0.57257 \dots + 2 πn

グラフ

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