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sec((13pi)/4)

الحلّ

sec (\frac{13 π}{4})

الحلّ

- 2

العشري

- 1.41421 \dots

خطوات الحلّ

sec (\frac{13 π}{4})

sec (\frac{13 π}{4}) = sec (\frac{5 π}{4})

sec (\frac{13 π}{4})

2 π + \frac{5 π}{4}

كـ

\frac{13 π}{4}

اكتب مجددًا

= sec (2 π + \frac{5 π}{4})

sec (x + 2 π) = sec (x)

sec :

استخدم دوريّة الـ

sec (2 π + \frac{5 π}{4}) = sec (\frac{5 π}{4})

= sec (\frac{5 π}{4})

= sec (\frac{5 π}{4})

Rewrite using trig identities:

\frac{1}{cos ( \frac{5 π}{4} )}

sec (\frac{5 π}{4})

sec (x) = \frac{1}{cos ( x )}

:Use the basic trigonometric identity

= \frac{1}{cos ( \frac{5 π}{4} )}

= \frac{1}{cos ( \frac{5 π}{4} )}

Rewrite using trig identities:

cos (\frac{5 π}{4}) = - \frac{2}{2}

cos (\frac{5 π}{4})

Rewrite using trig identities:

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

cos (\frac{5 π}{4})

cos (π + \frac{π}{4})

كـ

cos (\frac{5 π}{4})

أكتب

= cos (π + \frac{π}{4})

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

:فعّل متطابقة الجمع لزوايا

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

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

استخدم المتطابقة الأساسيّة التالية:

cos (π) = (- 1)

cos (π)

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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 (π) = 0

sin (π)

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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}

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

بسّط

= - \frac{2}{2}

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

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

بسّط:

- 2

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

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

: استخدم ميزات الكسور التالية

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

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

: استخدم ميزات الكسور التالية

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

= - \frac{2}{2}

: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}}

:فعْل قانون الجذور

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

= - 2

= - 2

أمثلة شائعة

sinh(pi/2)

sinh (\frac{π}{2})

cos^5(pi)

cos^{5} (π)

cot(3)

cot (3)

cot((25pi)/6)

cot (\frac{25 π}{6})

cos(5/6 pi)

cos (\frac{5}{6} π)