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شائع علم المثلثات >

2csc(x)+7/(cos(x))=0

الحلّ

2 csc (x) + \frac{7}{cos ( x )} = 0

الحلّ

x = 2.86329 \dots + πn

+1

درجات

x = 164.05460 \dots^{\circ} + 18 0^{\circ} n

خطوات الحلّ

2 csc (x) + \frac{7}{cos ( x )} = 0

2 csc (x) + \frac{7}{cos ( x )}

بسّط:

\frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )}

2 csc (x) + \frac{7}{cos ( x )}

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

:حوّل الأعداد لكسور

= \frac{2 csc ( x ) cos ( x )}{cos ( x )} + \frac{7}{cos ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )}

\frac{2 csc ( x ) cos ( x ) + 7}{cos ( x )} = 0

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

2 csc (x) cos (x) + 7 = 0

Rewrite using trig identities

2 csc (x) cos (x) + 7

csc (x) cos (x) = cot (x)

csc (x) cos (x)

sin, cos :

عبّر بواسطة

csc (x) cos (x)

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

:Use the basic trigonometric identity

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

\frac{1}{sin ( x )} cos (x)

بسّط:

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

\frac{1}{sin ( x )} cos (x)

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

:اضرب كسور

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

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

اضرب

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

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

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

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

:Use the basic trigonometric identity

= cot (x)

= 7 + 2 cot (x)

7 + 2 cot (x) = 0

انقل

7

إلى الجانب الأيمن

7 + 2 cot (x) = 0

من الطرفين

7

اطرح

7 + 2 cot (x) - 7 = 0 - 7

بسّط

2 cot (x) = - 7

2 cot (x) = - 7

2

اقسم الطرفين على

2 cot (x) = - 7

2

اقسم الطرفين على

\frac{2 cot ( x )}{2} = \frac{- 7}{2}

بسّط

cot (x) = - \frac{7}{2}

cot (x) = - \frac{7}{2}

Apply trig inverse properties

cot (x) = - \frac{7}{2}

cot (x) = - \frac{7}{2} :

حلول عامّة لـ

cot (x) = - a \Rightarrow x = arccot (- a) + πn

x = arccot (- \frac{7}{2}) + πn

x = arccot (- \frac{7}{2}) + πn

أظهر الحلّ بالتمثيل العشريّ

x = 2.86329 \dots + πn

رسم

أمثلة شائعة

(tan(θ)cot(θ))/(sec^2(θ))=cot(θ)

sin(y)=(sqrt(3))/2

9sin^2(x)+3cos(x)-7=0