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شائع علم المثلثات >

1/(cos(33)cos(12)-sin(33)sin(12))

الحلّ

\frac{1}{cos ( 3 3 ^{\circ} ) cos ( 1 2 ^{\circ} ) - sin ( 3 3 ^{\circ} ) sin ( 1 2 ^{\circ} )}

الحلّ

2

+1

عشري

1.41421 \dots

خطوات الحلّ

\frac{1}{cos ( 3 3 ^{\circ} ) cos ( 1 2 ^{\circ} ) - sin ( 3 3 ^{\circ} ) sin ( 1 2 ^{\circ} )}

Rewrite using trig identities:

cos (3 3^{\circ}) cos (1 2^{\circ}) - sin (3 3^{\circ}) sin (1 2^{\circ}) = cos (4 5^{\circ})

cos (3 3^{\circ}) cos (1 2^{\circ}) - sin (3 3^{\circ}) sin (1 2^{\circ})

cos (s) cos (t) - sin (s) sin (t) = cos (s + t)

:فعّل متطابقة الجمع لزوايا

= cos (3 3^{\circ} + 1 2^{\circ})

بسّط

= cos (4 5^{\circ})

= \frac{1}{cos ( 4 5 ^{\circ} )}

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}

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

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

بسّط:

2

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

\frac{1}{\frac{b}{c}} = \frac{c}{b}

: استخدم ميزات الكسور التالية

= \frac{2}{2}

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

:فعْل قانون الجذور

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

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

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

:فعّل قانون القوى

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

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

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

اطرح الأعداد

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

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

:فعْل قانون الجذور

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

= 2

= 2

أمثلة شائعة

arcsin (\frac{19}{32})

arcsin(cos(pi/2))

arcsin (cos (\frac{π}{2}))

cos^{2} (33 0^{\circ})

arctan (\frac{12}{4})

arctan((-3)/(sqrt(3)))

arctan (\frac{- 3}{3})