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شائع علم المثلثات >

7cot(θ)=3csc(θ)

الحلّ

7 cot (θ) = 3 csc (θ)

الحلّ

θ = 1.12788 \dots + 2 πn, θ = 2 π - 1.12788 \dots + 2 πn

+1

درجات

θ = 64.62306 \dots^{\circ} + 36 0^{\circ} n, θ = 295.37693 \dots^{\circ} + 36 0^{\circ} n

خطوات الحلّ

7 cot (θ) = 3 csc (θ)

من الطرفين

3 csc (θ)

اطرح

7 cot (θ) - 3 csc (θ) = 0

sin, cos :

عبّر بواسطة

- 3 csc (θ) + 7 cot (θ)

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

:Use the basic trigonometric identity

= - 3 \cdot \frac{1}{sin ( θ )} + 7 cot (θ)

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

:Use the basic trigonometric identity

= - 3 \cdot \frac{1}{sin ( θ )} + 7 \cdot \frac{cos ( θ )}{sin ( θ )}

- 3 \cdot \frac{1}{sin ( θ )} + 7 \cdot \frac{cos ( θ )}{sin ( θ )}

بسّط:

\frac{- 3 + 7 cos ( θ )}{sin ( θ )}

- 3 \cdot \frac{1}{sin ( θ )} + 7 \cdot \frac{cos ( θ )}{sin ( θ )}

3 \cdot \frac{1}{sin ( θ )} = \frac{3}{sin ( θ )}

3 \cdot \frac{1}{sin ( θ )}

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

:اضرب كسور

= \frac{1 \cdot 3}{sin ( θ )}

1 \cdot 3 = 3 :

اضرب الأعداد

= \frac{3}{sin ( θ )}

7 \cdot \frac{cos ( θ )}{sin ( θ )} = \frac{7 cos ( θ )}{sin ( θ )}

7 \cdot \frac{cos ( θ )}{sin ( θ )}

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

:اضرب كسور

= \frac{cos ( θ ) \cdot 7}{sin ( θ )}

= - \frac{3}{sin ( θ )} + \frac{7 cos ( θ )}{sin ( θ )}

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

فعّل القانون

= \frac{- 3 + 7 cos ( θ )}{sin ( θ )}

= \frac{- 3 + 7 cos ( θ )}{sin ( θ )}

\frac{- 3 + 7 cos ( θ )}{sin ( θ )} = 0

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

- 3 + 7 cos (θ) = 0

انقل

3

إلى الجانب الأيمن

- 3 + 7 cos (θ) = 0

للطرفين

3

أضف

- 3 + 7 cos (θ) + 3 = 0 + 3

بسّط

7 cos (θ) = 3

7 cos (θ) = 3

7

اقسم الطرفين على

7 cos (θ) = 3

7

اقسم الطرفين على

\frac{7 cos ( θ )}{7} = \frac{3}{7}

بسّط

cos (θ) = \frac{3}{7}

cos (θ) = \frac{3}{7}

Apply trig inverse properties

cos (θ) = \frac{3}{7}

cos (θ) = \frac{3}{7} :

حلول عامّة لـ

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

θ = arccos (\frac{3}{7}) + 2 πn, θ = 2 π - arccos (\frac{3}{7}) + 2 πn

θ = arccos (\frac{3}{7}) + 2 πn, θ = 2 π - arccos (\frac{3}{7}) + 2 πn

أظهر الحلّ بالتمثيل العشريّ

θ = 1.12788 \dots + 2 πn, θ = 2 π - 1.12788 \dots + 2 πn

رسم

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