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人気のある三角関数 >

solvefor t,v=311cos(30t+30)v

解

解く

t, v = 311 cos (30 t + 3 0^{\circ}) v

解

t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{1.56758 \dots}{30}, t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{1.56758 \dots}{30}

+1

ラジアン

t = - \frac{π}{180} + \frac{1.56758 \dots}{30} + \frac{π}{15} n, t = \frac{π}{15} - \frac{π}{180} - \frac{1.56758 \dots}{30} + \frac{π}{15} n

解答ステップ

v = 311 cos (30 t + 3 0^{\circ}) v

辺を交換する

311 cos (30 t + \frac{π}{6}) v = v

以下で両辺を割る

311 v; v \neq = 0

311 cos (30 t + \frac{π}{6}) v = v

以下で両辺を割る

311 v; v \neq = 0

\frac{311 cos ( 30 t + \frac{π}{6} ) v}{311 v} = \frac{v}{311 v}; v \neq = 0

簡素化

cos (30 t + \frac{π}{6}) = \frac{1}{311}; v \neq = 0

cos (30 t + \frac{π}{6}) = \frac{1}{311}; v \neq = 0

三角関数の逆数プロパティを適用する

cos (30 t + 3 0^{\circ}) = \frac{1}{311}

以下の一般解

cos (30 t + 3 0^{\circ}) = \frac{1}{311}

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

30 t + 3 0^{\circ} = arccos (\frac{1}{311}) + 36 0^{\circ} n, 30 t + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n

30 t + 3 0^{\circ} = arccos (\frac{1}{311}) + 36 0^{\circ} n, 30 t + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n

解く

30 t + 3 0^{\circ} = arccos (\frac{1}{311}) + 36 0^{\circ} n : t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}

30 t + 3 0^{\circ} = arccos (\frac{1}{311}) + 36 0^{\circ} n

3 0^{\circ}

を右側に移動します

30 t + 3 0^{\circ} = arccos (\frac{1}{311}) + 36 0^{\circ} n

両辺から

3 0^{\circ}

を引く

30 t + 3 0^{\circ} - 3 0^{\circ} = arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

簡素化

30 t = arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

30 t = arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

以下で両辺を割る

30

30 t = arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

以下で両辺を割る

30

\frac{30 t}{30} = \frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30}

簡素化

\frac{30 t}{30} = \frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30}

簡素化

\frac{30 t}{30} : t

\frac{30 t}{30}

数を割る:

\frac{30}{30} = 1

= t

簡素化

\frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30} : \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}

\frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30}

条件のようなグループ

= \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30} + \frac{arccos ( \frac{1}{311} )}{30}

\frac{36 0 ^{\circ} n}{30} = \frac{18 0 ^{\circ} n}{15}

\frac{36 0 ^{\circ} n}{30}

共通因数を約分する:

2

= \frac{18 0 ^{\circ} n}{15}

\frac{3 0 ^{\circ}}{30} = 1^{\circ}

\frac{3 0 ^{\circ}}{30}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{6 \cdot 30}

数を乗じる:

6 \cdot 30 = 180

= 1^{\circ}

= \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}

t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}

t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}

t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}

解く

30 t + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n : t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

30 t + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n

3 0^{\circ}

を右側に移動します

30 t + 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n

両辺から

3 0^{\circ}

を引く

30 t + 3 0^{\circ} - 3 0^{\circ} = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

簡素化

30 t = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

30 t = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

以下で両辺を割る

30

30 t = 36 0^{\circ} - arccos (\frac{1}{311}) + 36 0^{\circ} n - 3 0^{\circ}

以下で両辺を割る

30

\frac{30 t}{30} = 1 2^{\circ} - \frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30}

簡素化

\frac{30 t}{30} = 1 2^{\circ} - \frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30}

簡素化

\frac{30 t}{30} : t

\frac{30 t}{30}

数を割る:

\frac{30}{30} = 1

= t

簡素化

1 2^{\circ} - \frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30} : 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

1 2^{\circ} - \frac{arccos ( \frac{1}{311} )}{30} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30}

条件のようなグループ

= 1 2^{\circ} + \frac{36 0 ^{\circ} n}{30} - \frac{3 0 ^{\circ}}{30} - \frac{arccos ( \frac{1}{311} )}{30}

1 2^{\circ} = 1 2^{\circ}

1 2^{\circ}

共通因数を約分する:

2

= 1 2^{\circ}

\frac{36 0 ^{\circ} n}{30} = \frac{18 0 ^{\circ} n}{15}

\frac{36 0 ^{\circ} n}{30}

共通因数を約分する:

2

= \frac{18 0 ^{\circ} n}{15}

\frac{3 0 ^{\circ}}{30} = 1^{\circ}

\frac{3 0 ^{\circ}}{30}

分数の規則を適用する:

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

= \frac{18 0 ^{\circ}}{6 \cdot 30}

数を乗じる:

6 \cdot 30 = 180

= 1^{\circ}

= 1 2^{\circ} + \frac{18 0 ^{\circ} n}{15} - 1^{\circ} - \frac{arccos ( \frac{1}{311} )}{30}

条件のようなグループ

= 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{arccos ( \frac{1}{311} )}{30}, t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{arccos ( \frac{1}{311} )}{30}

10進法形式で解を証明する

t = \frac{18 0 ^{\circ} n}{15} - 1^{\circ} + \frac{1.56758 \dots}{30}, t = 1 2^{\circ} - 1^{\circ} + \frac{18 0 ^{\circ} n}{15} - \frac{1.56758 \dots}{30}

グラフ

人気の例

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