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شائع علم المثلثات >

(sin(45)+cos(45))/(sin^2(60))

الحلّ

\frac{sin ( 4 5 ^{\circ} ) + cos ( 4 5 ^{\circ} )}{sin ^{2} ( 6 0 ^{\circ} )}

الحلّ

\frac{4 2}{3}

+1

عشري

1.88561 \dots

خطوات الحلّ

\frac{sin ( 4 5 ^{\circ} ) + cos ( 4 5 ^{\circ} )}{sin ^{2} ( 6 0 ^{\circ} )}

استخدم المتطابقة الأساسيّة التالية:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\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{2}{2}

استخدم المتطابقة الأساسيّة التالية:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{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{2}{2} + \frac{2}{2}}{( \frac{3}{2} ) ^{2}}

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

بسّط:

\frac{4 2}{3}

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

\frac{2}{2} + \frac{2}{2}

وحّد الكسور:

2

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

فعّل القانون

= \frac{2 + 2}{2}

2 + 2 = 22 :

اجمع العناصر المتشابهة

= \frac{2 2}{2}

\frac{2}{2} = 1 :

اقسم الأعداد

= 2

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

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

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

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

:فعّل قانون القوى

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

(3)^{2} : 3

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

:فعْل قانون الجذور

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

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

:فعّل قانون القوى

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

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

\frac{1}{2} \cdot 2

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

:اضرب كسور

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

2 :

إلغ العوامل المشتركة

= 1

= 3

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

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

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

: استخدم ميزات الكسور التالية

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

2^{2} = 4

= \frac{4 2}{3}

= \frac{4 2}{3}

أمثلة شائعة

-sin(pi/4)+cos(pi/4)

- sin (\frac{π}{4}) + cos (\frac{π}{4})

arcsin(0.42288)

arcsin (0.42288)

arctan(sinh(7/20))

arctan (sinh (\frac{7}{20}))

sec (1) + tan (1)

2 + 2 sin (4 5^{\circ})