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شائع علم المثلثات >

(sin(55.01-x))/(sin(x))= 1200/500

الحلّ

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

الحلّ

x = 2.75168 \dots + πn

درجات

x = 157.65972 \dots^{\circ} + 18 0^{\circ} n

خطوات الحلّ

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Rewrite using trig identities

\frac{sin ( 55.01 - x )}{sin ( x )} = \frac{1200}{500}

Rewrite using trig identities

sin (55.01 - x)

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

:فعّل متطابقة الطرح لزوايا

= sin (55.01) cos (x) - cos (55.01) sin (x)

sin (55.01) cos (x) - cos (55.01) sin (x)

بسّط:

- 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

sin (55.01) cos (x) - cos (55.01) sin (x)

sin (55.01)

بسّط:

- 0.99948 \dots

sin (55.01)

sin (55.01) = - 0.99948 \dots

= - 0.99948 \dots

= - 0.99948 \dots cos (x) - cos (55.01) sin (x)

cos (55.01)

بسّط:

0.03212 \dots

cos (55.01)

cos (55.01) = 0.03212 \dots

= 0.03212 \dots

= - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

= - 0.99948 \dots cos (x) - 0.03212 \dots sin (x)

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{1200}{500}

\frac{1200}{500} = \frac{12}{5}

\frac{1200}{500}

100 :

إلغ العوامل المشتركة

= \frac{12}{5}

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{12}{5}

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} = \frac{12}{5}

من الطرفين

\frac{12}{5}

اطرح

\frac{- 0.99948 \dots cos ( x ) - 0.03212 \dots sin ( x )}{sin ( x )} - 2.4 = 0

Rewrite using trig identities

- 2.4 + \frac{- 0.03212 \dots sin ( x ) - 0.99948 \dots cos ( x )}{sin ( x )}

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

:Use the basic trigonometric identity

= - 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

- 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

بسّط:

- 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

- 2.4 + \frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

\frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}} = csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

\frac{- 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x )}{\frac{1}{c s c ( x )}}

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

: استخدم ميزات الكسور التالية

= \frac{( - 0.03212 \dots \cdot \frac{1}{c s c ( x )} - 0.99948 \dots cos ( x ) ) csc ( x )}{1}

0.03212 \dots \cdot \frac{1}{csc ( x )} = \frac{0.03212 \dots}{csc ( x )}

0.03212 \dots \cdot \frac{1}{csc ( x )}

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

:اضرب كسور

= \frac{1 \cdot 0.03212 \dots}{csc ( x )}

1 \cdot 0.03212 \dots = 0.03212 \dots :

اضرب الأعداد

= \frac{0.03212 \dots}{csc ( x )}

= \frac{csc ( x ) ( - \frac{0.03212 \dots}{c s c ( x )} - 0.99948 \dots cos ( x ) )}{1}

\frac{a}{1} = a

: استخدم ميزات الكسور التالية

= (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x)) csc (x)

= - 2.4 + csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

= - 2.4 + csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

وسٌع:

- 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

csc (x) (- \frac{0.03212 \dots}{csc ( x )} - 0.99948 \dots cos (x))

a (b - c) = ab - a c

: افتح أقواس بالاستعانة بـ

a = csc (x), b = - \frac{0.03212 \dots}{csc ( x )}, c = 0.99948 \dots cos (x)

= csc (x) (- \frac{0.03212 \dots}{csc ( x )}) - csc (x) \cdot 0.99948 \dots cos (x)

فعّل قوانين سالب-موجب

+ (- a) = - a

= - \frac{0.03212 \dots}{csc ( x )} csc (x) - 0.99948 \dots csc (x) cos (x)

\frac{0.03212 \dots}{csc ( x )} csc (x) = 0.03212 \dots

\frac{0.03212 \dots}{csc ( x )} csc (x)

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

:اضرب كسور

= \frac{0.03212 \dots csc ( x )}{csc ( x )}

csc (x) :

إلغ العوامل المشتركة

= 0.03212 \dots

= - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

= - 2.4 - 0.03212 \dots - 0.99948 \dots csc (x) cos (x)

- 2.4 - 0.03212 \dots = - 2.43212 \dots :

اطرح الأعداد

= - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

= - 0.99948 \dots csc (x) cos (x) - 2.43212 \dots

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)

= - 2.43212 \dots - 0.99948 \dots cot (x)

- 2.43212 \dots - 0.99948 \dots cot (x) = 0

انقل

2.43212 \dots

إلى الجانب الأيمن

- 2.43212 \dots - 0.99948 \dots cot (x) = 0

للطرفين

2.43212 \dots

أضف

- 2.43212 \dots - 0.99948 \dots cot (x) + 2.43212 \dots = 0 + 2.43212 \dots

بسّط

- 0.99948 \dots cot (x) = 2.43212 \dots

- 0.99948 \dots cot (x) = 2.43212 \dots

- 0.99948 \dots

اقسم الطرفين على

- 0.99948 \dots cot (x) = 2.43212 \dots

- 0.99948 \dots

اقسم الطرفين على

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} = \frac{2.43212 \dots}{- 0.99948 \dots}

بسّط

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots} = \frac{2.43212 \dots}{- 0.99948 \dots}

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots}

بسّط:

cot (x)

\frac{- 0.99948 \dots cot ( x )}{- 0.99948 \dots}

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

: استخدم ميزات الكسور التالية

= \frac{0.99948 \dots cot ( x )}{0.99948 \dots}

0.99948 \dots :

إلغ العوامل المشتركة

= cot (x)

\frac{2.43212 \dots}{- 0.99948 \dots}

بسّط:

- 2.43337 \dots

\frac{2.43212 \dots}{- 0.99948 \dots}

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

: استخدم ميزات الكسور التالية

= - \frac{2.43212 \dots}{0.99948 \dots}

\frac{2.43212 \dots}{0.99948 \dots} = 2.43337 \dots :

اقسم الأعداد

= - 2.43337 \dots

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots

Apply trig inverse properties

cot (x) = - 2.43337 \dots

cot (x) = - 2.43337 \dots :

حلول عامّة لـ

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

x = arccot (- 2.43337 \dots) + πn

x = arccot (- 2.43337 \dots) + πn

أظهر الحلّ بالتمثيل العشريّ

x = 2.75168 \dots + πn

رسم

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