English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

(tan^2(30)sec(45))/(1/(sin^2(60)))

الحلّ

\frac{tan ^{2} ( 3 0 ^{\circ} ) sec ( 4 5 ^{\circ} )}{\frac{1}{s i n ^{2} ( 6 0 ^{\circ} )}}

الحلّ

\frac{2}{4}

عشري

0.35355 \dots

خطوات الحلّ

\frac{tan ^{2} ( 3 0 ^{\circ} ) sec ( 4 5 ^{\circ} )}{\frac{1}{s i n ^{2} ( 6 0 ^{\circ} )}}

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 (4 5^{\circ}) = 2

sec (4 5^{\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:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 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{3}{2}

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

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

بسّط:

\frac{2}{4}

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

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

: استخدم ميزات الكسور التالية

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

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

(\frac{3}{3})^{2} 2 (\frac{3}{2})^{2}

a^{m} b^{m} = (ab)^{m}

:فعّل قانون القوى

(\frac{3}{3})^{2} (\frac{3}{2})^{2} = (\frac{3}{3} \cdot \frac{3}{2})^{2}

= 2 (\frac{3}{3} \cdot \frac{3}{2})^{2}

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

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

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

\frac{3}{3}

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

:فعْل قانون الجذور

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

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

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

اطرح الأعداد

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

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

:فعْل قانون الجذور

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

= \frac{1}{3}

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

3

اختزل قطريًا

= \frac{1}{2}

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

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

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

(\frac{1}{2})^{2}

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

:فعّل قانون القوى

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

1^{a} = 1

فعّل القانون

1^{2} = 1

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

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

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

اضرب بـ:

\frac{1}{2 2}

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

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

:اضرب كسور

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

1 \cdot 2 = 2 :

اضرب

= \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}}}

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}}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

= \frac{1}{2 2}

\frac{1}{2 2}

حوّل لصيغة عدد كسريّ:

\frac{2}{4}

\frac{1}{2 2}

\frac{2}{2}

اضرب بالمرافق

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

1 \cdot 2 = 2

222 = 4

222

a^{b} \cdot a^{c} = a^{b + c}

:فعّل قانون القوى

222 = 2 \cdot 2^{\frac{1}{2}} \cdot 2^{\frac{1}{2}} = 2^{1 + \frac{1}{2} + \frac{1}{2}}

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

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

اجمع العناصر المتشابهة

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

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

2 \cdot \frac{1}{2}

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

:اضرب كسور

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

2 :

إلغ العوامل المشتركة

= 1

= 2^{1 + 1}

1 + 1 = 2 :

اجمع الأعداد

= 2^{2}

2^{2} = 4

= 4

= \frac{2}{4}

= \frac{2}{4}

= \frac{2}{4}

أمثلة شائعة

arccos(63/65)

arccos (\frac{63}{65})

sin(20)cos(10)

sin (2 0^{\circ}) cos (1 0^{\circ})

(8sin(45))/5

\frac{8 sin ( 4 5 ^{\circ} )}{5}

(cot^2(1/2))/(cot^2(10/2))

\frac{cot ^{2} ( \frac{1 ^{\circ}}{2} )}{cot ^{2} ( \frac{1 0 ^{\circ}}{2} )}

arcsin(0.56051)

arcsin (0.56051)