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شائع علم المثلثات >

sec(2x-10)=csc(32)

الحلّ

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

الحلّ

x = 18 0^{\circ} n + 5^{\circ} + \frac{1.01229 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{1.01229 \dots}{2}

+1

راديان

x = \frac{π}{36} + \frac{1.01229 \dots}{2} + πn, x = π + \frac{π}{36} - \frac{1.01229 \dots}{2} + πn

خطوات الحلّ

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

Apply trig inverse properties

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ})

sec (2 x - 1 0^{\circ}) = csc (3 2^{\circ}) :

حلول عامّة لـ

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 (3 2^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n, 2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

حلّ:

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

انقل

1 0^{\circ}

إلى الجانب الأيمن

2 x - 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

للطرفين

1 0^{\circ}

أضف

2 x - 1 0^{\circ} + 1 0^{\circ} = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

بسّط

2 x = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2

اقسم الطرفين على

2 x = arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2

اقسم الطرفين على

\frac{2 x}{2} = \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

بسّط

\frac{2 x}{2} = \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

\frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

بسّط:

18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

\frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

جمّع التعابير المتشابهة

= \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

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

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

\frac{2}{2} = 1 :

اقسم الأعداد

= 18 0^{\circ} n

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

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

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

: استخدم ميزات الكسور التالية

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

18 \cdot 2 = 36 :

اضرب الأعداد

= 5^{\circ}

= 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

حلّ:

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

انقل

1 0^{\circ}

إلى الجانب الأيمن

2 x - 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n

للطرفين

1 0^{\circ}

أضف

2 x - 1 0^{\circ} + 1 0^{\circ} = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

بسّط

2 x = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2 x = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2

اقسم الطرفين على

2 x = 36 0^{\circ} - arcsec (csc (3 2^{\circ})) + 36 0^{\circ} n + 1 0^{\circ}

2

اقسم الطرفين على

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

بسّط

\frac{2 x}{2} = 18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

\frac{2 x}{2}

بسّط:

x

\frac{2 x}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= x

18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

بسّط:

18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

18 0^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2}

جمّع التعابير المتشابهة

= 18 0^{\circ} + \frac{36 0 ^{\circ} n}{2} + \frac{1 0 ^{\circ}}{2} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

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

18 0^{\circ}

\frac{2}{2} = 1 :

اقسم الأعداد

= 18 0^{\circ}

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

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

\frac{2}{2} = 1 :

اقسم الأعداد

= 18 0^{\circ} n

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

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

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

: استخدم ميزات الكسور التالية

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

18 \cdot 2 = 36 :

اضرب الأعداد

= 5^{\circ}

= 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

x = 18 0^{\circ} n + 5^{\circ} + \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{arcsec ( csc ( 3 2 ^{\circ} ) )}{2}

أظهر الحلّ بالتمثيل العشريّ

x = 18 0^{\circ} n + 5^{\circ} + \frac{1.01229 \dots}{2}, x = 18 0^{\circ} + 18 0^{\circ} n + 5^{\circ} - \frac{1.01229 \dots}{2}

رسم

أمثلة شائعة

4 = cos (x)

solvefor x,e^{4y}=cos(4x+y)

so l v e f or x, e^{4 y} = cos (4 x + y)

3tan(2x)-3cot(x)=0

3 tan (2 x) - 3 cot (x) = 0

cos (θ) = (\frac{1}{4})

(36)/(sin(110))=(15)/(sin(x))

\frac{36}{sin ( 11 0 ^{\circ} )} = \frac{15}{sin ( x )}