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csc(-300)

الحلّ

csc (- 30 0^{\circ})

الحلّ

\frac{2 3}{3}

العشري

1.15470 \dots

خطوات الحلّ

csc (- 30 0^{\circ})

csc (- x) = - csc (x) :

استخدم القانون التالي

csc (- 30 0^{\circ}) = - csc (30 0^{\circ})

= - csc (30 0^{\circ})

Rewrite using trig identities:

csc (30 0^{\circ}) = - \frac{2 3}{3}

csc (30 0^{\circ})

Rewrite using trig identities:

\frac{1}{sin ( 30 0 ^{\circ} )}

csc (30 0^{\circ})

csc (x) = \frac{1}{sin ( x )}

:Use the basic trigonometric identity

= \frac{1}{sin ( 30 0 ^{\circ} )}

= \frac{1}{sin ( 30 0 ^{\circ} )}

Rewrite using trig identities:

sin (30 0^{\circ}) = - \frac{3}{2}

sin (30 0^{\circ})

Rewrite using trig identities:

sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

sin (30 0^{\circ})

sin (18 0^{\circ} + 12 0^{\circ})

كـ

sin (30 0^{\circ})

أكتب

= sin (18 0^{\circ} + 12 0^{\circ})

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

:فعّل متطابقة الجمع لزوايا

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

= sin (18 0^{\circ}) cos (12 0^{\circ}) + cos (18 0^{\circ}) sin (12 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (18 0^{\circ}) = 0

sin (18 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}

= 0

استخدم المتطابقة الأساسيّة التالية:

cos (12 0^{\circ}) = - \frac{1}{2}

cos (12 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:

cos (18 0^{\circ}) = (- 1)

cos (18 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}

= (- 1)

استخدم المتطابقة الأساسيّة التالية:

sin (12 0^{\circ}) = \frac{3}{2}

sin (12 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}

= 0 \cdot (- \frac{1}{2}) + (- 1) \frac{3}{2}

بسّط

= - \frac{3}{2}

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

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

بسّط:

- \frac{2 3}{3}

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

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

: استخدم ميزات الكسور التالية

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

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

: استخدم ميزات الكسور التالية

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

= - \frac{2}{3}

- \frac{2}{3}

حوّل لصيغة عدد كسريّ:

- \frac{2 3}{3}

- \frac{2}{3}

\frac{3}{3}

اضرب بالمرافق

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

33 = 3

33

a a = a

:فعْل قانون الجذور

33 = 3

= 3

= - \frac{2 3}{3}

= - \frac{2 3}{3}

= - \frac{2 3}{3}

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

بسّط

= \frac{2 3}{3}

أمثلة شائعة

30sin(60)

30 sin (6 0^{\circ})

arctan(9/6)

arctan (\frac{9}{6})

arcsin(cos(-(7pi)/6))

arcsin (cos (- \frac{7 π}{6}))

tan((-4pi)/3)

tan (\frac{- 4 π}{3})

arccos(30)

arccos (30)