English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

sec^2(a)cot(a)=8

الحلّ

sec^{2} (a) cot (a) = 8

الحلّ

a = \frac{0.25268 \dots}{2} + πn, a = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

درجات

a = 7.23875 \dots^{\circ} + 18 0^{\circ} n, a = 82.76124 \dots^{\circ} + 18 0^{\circ} n

خطوات الحلّ

sec^{2} (a) cot (a) = 8

من الطرفين

8

اطرح

sec^{2} (a) cot (a) - 8 = 0

sin, cos :

عبّر بواسطة

- 8 + cot (a) sec^{2} (a)

cot (x) = \frac{cos ( x )}{sin ( x )}

:Use the basic trigonometric identity

= - 8 + \frac{cos ( a )}{sin ( a )} sec^{2} (a)

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

:Use the basic trigonometric identity

= - 8 + \frac{cos ( a )}{sin ( a )} (\frac{1}{cos ( a )})^{2}

- 8 + \frac{cos ( a )}{sin ( a )} (\frac{1}{cos ( a )})^{2}

بسّط:

\frac{- 8 cos ( a ) sin ( a ) + 1}{cos ( a ) sin ( a )}

- 8 + \frac{cos ( a )}{sin ( a )} (\frac{1}{cos ( a )})^{2}

\frac{cos ( a )}{sin ( a )} (\frac{1}{cos ( a )})^{2} = \frac{1}{cos ( a ) sin ( a )}

\frac{cos ( a )}{sin ( a )} (\frac{1}{cos ( a )})^{2}

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

:اضرب كسور

= \frac{cos ( a ) ( \frac{1}{c o s ( a )} ) ^{2}}{sin ( a )}

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

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

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

:فعّل قانون القوى

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

1^{a} = 1

فعّل القانون

1^{2} = 1

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

= \frac{\frac{1}{c o s ^{2} ( a )} cos ( a )}{sin ( a )}

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

اضرب بـ:

\frac{1}{cos ( a )}

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

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

:اضرب كسور

= \frac{1 \cdot cos ( a )}{cos ^{2} ( a )}

1 \cdot cos (a) = cos (a) :

اضرب

= \frac{cos ( a )}{cos ^{2} ( a )}

cos (a) :

إلغ العوامل المشتركة

= \frac{1}{cos ( a )}

= \frac{\frac{1}{c o s ( a )}}{sin ( a )}

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

: استخدم ميزات الكسور التالية

= \frac{1}{cos ( a ) sin ( a )}

= - 8 + \frac{1}{cos ( a ) sin ( a )}

8 = \frac{8 cos ( a ) sin ( a )}{cos ( a ) sin ( a )}

:حوّل الأعداد لكسور

= - \frac{8 cos ( a ) sin ( a )}{cos ( a ) sin ( a )} + \frac{1}{cos ( a ) sin ( a )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- 8 cos ( a ) sin ( a ) + 1}{cos ( a ) sin ( a )}

= \frac{- 8 cos ( a ) sin ( a ) + 1}{cos ( a ) sin ( a )}

\frac{1 - 8 cos ( a ) sin ( a )}{cos ( a ) sin ( a )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

1 - 8 cos (a) sin (a) = 0

Rewrite using trig identities

1 - 8 cos (a) sin (a)

2 sin (x) cos (x) = sin (2 x)

:فعّل متطابقة الزاوية المضاعفة

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= 1 - 8 \cdot \frac{sin ( 2 a )}{2}

1 - 8 \cdot \frac{sin ( 2 a )}{2} = 0

8 \cdot \frac{sin ( 2 a )}{2} = 4 sin (2 a)

8 \cdot \frac{sin ( 2 a )}{2}

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

:اضرب كسور

= \frac{sin ( 2 a ) \cdot 8}{2}

\frac{8}{2} = 4 :

اقسم الأعداد

= 4 sin (2 a)

1 - 4 sin (2 a) = 0

انقل

1

إلى الجانب الأيمن

1 - 4 sin (2 a) = 0

من الطرفين

1

اطرح

1 - 4 sin (2 a) - 1 = 0 - 1

بسّط

- 4 sin (2 a) = - 1

- 4 sin (2 a) = - 1

- 4

اقسم الطرفين على

- 4 sin (2 a) = - 1

- 4

اقسم الطرفين على

\frac{- 4 sin ( 2 a )}{- 4} = \frac{- 1}{- 4}

بسّط

sin (2 a) = \frac{1}{4}

sin (2 a) = \frac{1}{4}

Apply trig inverse properties

sin (2 a) = \frac{1}{4}

sin (2 a) = \frac{1}{4} :

حلول عامّة لـ

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

2 a = arcsin (\frac{1}{4}) + 2 πn, 2 a = π - arcsin (\frac{1}{4}) + 2 πn

2 a = arcsin (\frac{1}{4}) + 2 πn, 2 a = π - arcsin (\frac{1}{4}) + 2 πn

2 a = arcsin (\frac{1}{4}) + 2 πn

حلّ:

a = \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 a = arcsin (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

2 a = arcsin (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

\frac{2 a}{2} = \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

بسّط

a = \frac{arcsin ( \frac{1}{4} )}{2} + πn

a = \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 a = π - arcsin (\frac{1}{4}) + 2 πn

حلّ:

a = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

2 a = π - arcsin (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

2 a = π - arcsin (\frac{1}{4}) + 2 πn

2

اقسم الطرفين على

\frac{2 a}{2} = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + \frac{2 πn}{2}

بسّط

a = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

a = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

a = \frac{arcsin ( \frac{1}{4} )}{2} + πn, a = \frac{π}{2} - \frac{arcsin ( \frac{1}{4} )}{2} + πn

أظهر الحلّ بالتمثيل العشريّ

a = \frac{0.25268 \dots}{2} + πn, a = \frac{π}{2} - \frac{0.25268 \dots}{2} + πn

رسم

أمثلة شائعة

6cos(x)+2=0

6 cos (x) + 2 = 0

solvefor y,ln(sin^2(3x))=e^x+arccot(y)

so l v e f or y, ln (sin^{2} (3 x)) = e^{x} + arccot (y)

cos(A)= 8/15

cos (A) = \frac{8}{15}

cot^2(θ)-1=csc^2(θ)

cot^{2} (θ) - 1 = csc^{2} (θ)

sec(4x)-sec(2x)=2

sec (4 x) - sec (2 x) = 2