English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

(sin(30)cos(60)csc(45))/(tan(30)sec(60)cot(45))

الحلّ

\frac{sin ( 3 0 ^{\circ} ) \cdot cos ( 6 0 ^{\circ} ) \cdot csc ( 4 5 ^{\circ} )}{tan ( 3 0 ^{\circ} ) \cdot sec ( 6 0 ^{\circ} ) \cdot cot ( 4 5 ^{\circ} )}

الحلّ

\frac{6}{8}

عشري

0.30618 \dots

خطوات الحلّ

\frac{sin ( 3 0 ^{\circ} ) cos ( 6 0 ^{\circ} ) csc ( 4 5 ^{\circ} )}{tan ( 3 0 ^{\circ} ) sec ( 6 0 ^{\circ} ) cot ( 4 5 ^{\circ} )}

استخدم المتطابقة الأساسيّة التالية:

sin (3 0^{\circ}) = \frac{1}{2}

sin (3 0^{\circ})

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

استخدم المتطابقة الأساسيّة التالية:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

استخدم المتطابقة الأساسيّة التالية:

csc (4 5^{\circ}) = 2

csc (4 5^{\circ})

csc (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

استخدم المتطابقة الأساسيّة التالية:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

استخدم المتطابقة الأساسيّة التالية:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

استخدم المتطابقة الأساسيّة التالية:

cot (4 5^{\circ}) = 1

cot (4 5^{\circ})

cot (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 1

= \frac{\frac{1}{2} \cdot \frac{1}{2} 2}{\frac{3}{3} \cdot 2 \cdot 1}

\frac{\frac{1}{2} \cdot \frac{1}{2} 2}{\frac{3}{3} \cdot 2 \cdot 1}

بسّط:

\frac{6}{8}

\frac{\frac{1}{2} \cdot \frac{1}{2} 2}{\frac{3}{3} \cdot 2 \cdot 1}

2 \cdot 1 = 2 :

اضرب الأعداد

= \frac{2 \frac{1}{2} \cdot \frac{1}{2}}{2 \cdot \frac{3}{3}}

2 \cdot \frac{3}{3}

اضرب بـ:

\frac{2}{3}

2 \cdot \frac{3}{3}

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

:اضرب كسور

= \frac{3 \cdot 2}{3}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

3 = 3^{\frac{1}{2}}

= \frac{2 \cdot 3 ^{\frac{1}{2}}}{3}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

\frac{3 ^{\frac{1}{2}}}{3 ^{1}} = \frac{1}{3 ^{1 - \frac{1}{2}}}

= \frac{2}{3 ^{1 - \frac{1}{2}}}

1 - \frac{1}{2} = \frac{1}{2} :

اطرح الأعداد

= \frac{2}{3 ^{\frac{1}{2}}}

a^{\frac{1}{n}} = n a

:فعْل قانون الجذور

3^{\frac{1}{2}} = 3

= \frac{2}{3}

= \frac{2 \frac{1}{2} \cdot \frac{1}{2}}{\frac{2}{3}}

\frac{1}{2} \cdot \frac{1}{2} 2

اضرب بـ:

\frac{1}{2 2}

\frac{1}{2} \cdot \frac{1}{2} 2

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

:اضرب كسور

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

1 \cdot 1 \cdot 2 = 2 :

اضرب

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

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{2}{4}

4

حلل إلى عوامل:

2^{2}

4 = 2^{2}

حلّل إلى عوامل

= \frac{2}{2 ^{2}}

\frac{2}{2 ^{2}}

اختزل:

\frac{1}{2 ^{\frac{3}{2}}}

\frac{2}{2 ^{2}}

n a = a^{\frac{1}{n}}

:فعْل قانون الجذور

2 = 2^{\frac{1}{2}}

= \frac{2 ^{\frac{1}{2}}}{2 ^{2}}

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

:فعّل قانون القوى

\frac{2 ^{\frac{1}{2}}}{2 ^{2}} = \frac{1}{2 ^{2 - \frac{1}{2}}}

= \frac{1}{2 ^{2 - \frac{1}{2}}}

2 - \frac{1}{2} = \frac{3}{2} :

اطرح الأعداد

= \frac{1}{2 ^{\frac{3}{2}}}

= \frac{1}{2 ^{\frac{3}{2}}}

2^{\frac{3}{2}} = 22

2^{\frac{3}{2}}

2^{\frac{3}{2}} = 2^{1 + \frac{1}{2}}

= 2^{1 + \frac{1}{2}}

x^{a + b} = x^{a} x^{b}

:فعّل قانون القوى

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

بسّط

= 22

= \frac{1}{2 2}

= \frac{\frac{1}{2 2}}{\frac{2}{3}}

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

:اقسم الكسور

= \frac{1 \cdot 3}{2 2 \cdot 2}

بسّط

= \frac{3}{2 2 \cdot 2}

2 \cdot 2 = 4 :

اضرب الأعداد

= \frac{3}{4 2}

\frac{3}{4 2}

حوّل لصيغة عدد كسريّ:

\frac{6}{8}

\frac{3}{4 2}

\frac{2}{2}

اضرب بالمرافق

= \frac{3 2}{4 2 2}

32 = 6

32

a b = a \cdot b

:فعْل قانون الجذور

32 = 3 \cdot 2

= 3 \cdot 2

3 \cdot 2 = 6 :

اضرب الأعداد

= 6

422 = 8

422

a a = a

:فعْل قانون الجذور

22 = 2

= 4 \cdot 2

4 \cdot 2 = 8 :

اضرب الأعداد

= 8

= \frac{6}{8}

= \frac{6}{8}

= \frac{6}{8}

أمثلة شائعة

tan^2(45-34/2)

tan^{2} (4 5^{\circ} - \frac{34}{2})

arctan((sqrt(15))/7)

arctan (\frac{15}{7})

cos(arcsin(-8/17))

cos (arcsin (- \frac{8}{17}))

sin(23.58)

sin (23.5 8^{\circ})

-3.521sin(0.503(6-6.75))

- 3.521 sin (0.503 (6 - 6.75))

(sin(30)*cos(60)*csc(45))/(tan(30)*sec(60)*cot(45))

الحلّ

الحلّ

أمثلة شائعة

(sin(30)cos(60)csc(45))/(tan(30)sec(60)cot(45))