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人気のある三角関数 >

solvefor x,sqrt(3)sec(5x)-2=0

解

解く

x, 3 sec (5 x) - 2 = 0

解

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

+1

度

x = 6^{\circ} + 7 2^{\circ} n, x = 6 6^{\circ} + 7 2^{\circ} n

解答ステップ

3 sec (5 x) - 2 = 0

2

を右側に移動します

3 sec (5 x) - 2 = 0

両辺に

2

を足す

3 sec (5 x) - 2 + 2 = 0 + 2

簡素化

3 sec (5 x) = 2

3 sec (5 x) = 2

以下で両辺を割る

3

3 sec (5 x) = 2

以下で両辺を割る

3

\frac{3 sec ( 5 x )}{3} = \frac{2}{3}

簡素化

\frac{3 sec ( 5 x )}{3} = \frac{2}{3}

簡素化

\frac{3 sec ( 5 x )}{3} : sec (5 x)

\frac{3 sec ( 5 x )}{3}

共通因数を約分する:

3

= sec (5 x)

簡素化

\frac{2}{3} : \frac{2 3}{3}

\frac{2}{3}

共役で乗じる

\frac{3}{3}

= \frac{2 3}{3 3}

33 = 3

33

累乗根の規則を適用する:

a a = a

33 = 3

= 3

= \frac{2 3}{3}

sec (5 x) = \frac{2 3}{3}

sec (5 x) = \frac{2 3}{3}

sec (5 x) = \frac{2 3}{3}

以下の一般解

sec (5 x) = \frac{2 3}{3}

sec (x)

2 πn

循環を含む周期性テーブル :

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

5 x = \frac{π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

5 x = \frac{π}{6} + 2 πn, 5 x = \frac{11 π}{6} + 2 πn

解く

5 x = \frac{π}{6} + 2 πn : x = \frac{π}{30} + \frac{2 πn}{5}

5 x = \frac{π}{6} + 2 πn

以下で両辺を割る

5

5 x = \frac{π}{6} + 2 πn

以下で両辺を割る

5

\frac{5 x}{5} = \frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

簡素化

\frac{5 x}{5} = \frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

\frac{\frac{π}{6}}{5} + \frac{2 πn}{5} : \frac{π}{30} + \frac{2 πn}{5}

\frac{\frac{π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{π}{6}}{5} = \frac{π}{30}

\frac{\frac{π}{6}}{5}

分数の規則を適用する:

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

= \frac{π}{6 \cdot 5}

数を乗じる:

6 \cdot 5 = 30

= \frac{π}{30}

= \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}

解く

5 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{30} + \frac{2 πn}{5}

5 x = \frac{11 π}{6} + 2 πn

以下で両辺を割る

5

5 x = \frac{11 π}{6} + 2 πn

以下で両辺を割る

5

\frac{5 x}{5} = \frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

簡素化

\frac{5 x}{5} = \frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

簡素化

\frac{5 x}{5} : x

\frac{5 x}{5}

数を割る:

\frac{5}{5} = 1

= x

簡素化

\frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5} : \frac{11 π}{30} + \frac{2 πn}{5}

\frac{\frac{11 π}{6}}{5} + \frac{2 πn}{5}

\frac{\frac{11 π}{6}}{5} = \frac{11 π}{30}

\frac{\frac{11 π}{6}}{5}

分数の規則を適用する:

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

= \frac{11 π}{6 \cdot 5}

数を乗じる:

6 \cdot 5 = 30

= \frac{11 π}{30}

= \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{11 π}{30} + \frac{2 πn}{5}

x = \frac{π}{30} + \frac{2 πn}{5}, x = \frac{11 π}{30} + \frac{2 πn}{5}

グラフ

人気の例

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sin (x) = \frac{14}{16}

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