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Популярное Тригонометрия >

sec(2x-10)=csc(50)

Решение

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

Решение

x = 18 0^{\circ} n + 5^{\circ} + \frac{0.69813 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{0.69813 \dots}{2}

Радианы

x = \frac{π}{36} + \frac{0.69813 \dots}{2} + πn, x = π + \frac{π}{36} - \frac{0.69813 \dots}{2} + πn

Шаги решения

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

Примените обратные тригонометрические свойства

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

Общие решения для

sec (2 x - 1 0^{\circ}) = csc (5 0^{\circ})

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

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

Решить

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

Переместите

1 0^{\circ}

вправо

2 x - 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

Добавьте

1 0^{\circ}

к обеим сторонам

2 x - 1 0^{\circ} + 1 0^{\circ} = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

После упрощения получаем

2 x = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Разделите обе стороны на

2

2 x = arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Разделите обе стороны на

2

\frac{2 x}{2} = \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

После упрощения получаем

\frac{2 x}{2} = \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Упростите

\frac{2 x}{2} : x

\frac{2 x}{2}

Разделите числа:

\frac{2}{2} = 1

= x

Упростите

\frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

\frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Сгруппируйте похожие слагаемые

= \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Разделите числа:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{1 0 ^{\circ}}{2} = 5^{\circ}

\frac{1 0 ^{\circ}}{2}

Примените правило дробей:

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

= \frac{18 0 ^{\circ}}{18 \cdot 2}

Перемножьте числа:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

Решить

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n : x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

Переместите

1 0^{\circ}

вправо

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n

Добавьте

1 0^{\circ}

к обеим сторонам

2 x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

После упрощения получаем

2 x = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Разделите обе стороны на

2

2 x = 36 0^{\circ} - arcsec (csc (5 0^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

Разделите обе стороны на

2

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

После упрощения получаем

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Упростите

\frac{2 x}{2} : x

\frac{2 x}{2}

Разделите числа:

\frac{2}{2} = 1

= x

Упростите

18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} : 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

18 0^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

Сгруппируйте похожие слагаемые

= 18 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

18 0^{\circ} = 18 0^{\circ}

18 0^{\circ}

Разделите числа:

\frac{2}{2} = 1

= 18 0^{\circ}

\frac{36 0 ^{\circ} n}{2} = 18 0^{\circ} n

\frac{36 0 ^{\circ} n}{2}

Разделите числа:

\frac{2}{2} = 1

= 18 0^{\circ} n

\frac{1 0 ^{\circ}}{2} = 5^{\circ}

\frac{1 0 ^{\circ}}{2}

Примените правило дробей:

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

= \frac{18 0 ^{\circ}}{18 \cdot 2}

Перемножьте числа:

18 \cdot 2 = 36

= 5^{\circ}

= 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 5 0 ^{\circ} ) )}{2}

Покажите решения в десятичной форме

x = 18 0^{\circ} n + 5^{\circ} + \frac{0.69813 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{0.69813 \dots}{2}

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