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شائع علم المثلثات >

csc(x)= 1/(sec(x))

الحلّ

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

الحلّ

x \in R لا يوجد حلّ لـ

خطوات الحلّ

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

من الطرفين

\frac{1}{sec ( x )}

اطرح

csc (x) - \frac{1}{sec ( x )} = 0

csc (x) - \frac{1}{sec ( x )}

بسّط:

\frac{csc ( x ) sec ( x ) - 1}{sec ( x )}

csc (x) - \frac{1}{sec ( x )}

csc (x) = \frac{csc ( x ) sec ( x )}{sec ( x )}

:حوّل الأعداد لكسور

= \frac{csc ( x ) sec ( x )}{sec ( x )} - \frac{1}{sec ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{csc ( x ) sec ( x ) - 1}{sec ( x )}

\frac{csc ( x ) sec ( x ) - 1}{sec ( x )} = 0

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

csc (x) sec (x) - 1 = 0

sin, cos :

عبّر بواسطة

- 1 + csc (x) sec (x)

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

:Use the basic trigonometric identity

= - 1 + \frac{1}{sin ( x )} sec (x)

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

:Use the basic trigonometric identity

= - 1 + \frac{1}{sin ( x )} \cdot \frac{1}{cos ( x )}

- 1 + \frac{1}{sin ( x )} \cdot \frac{1}{cos ( x )}

بسّط:

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

- 1 + \frac{1}{sin ( x )} \cdot \frac{1}{cos ( x )}

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

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

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

:اضرب كسور

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

1 \cdot 1 = 1 :

اضرب الأعداد

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

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

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

:حوّل الأعداد لكسور

= - \frac{1 \cdot sin ( x ) cos ( x )}{sin ( x ) cos ( x )} + \frac{1}{sin ( x ) cos ( x )}

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

:بما أنّ المقامات متساوية، اجمع البسوط

= \frac{- 1 \cdot sin ( x ) cos ( x ) + 1}{sin ( x ) cos ( x )}

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

اضرب

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

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

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

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

1 - cos (x) sin (x) = 0

Rewrite using trig identities

1 - cos (x) sin (x)

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

:فعّل متطابقة الزاوية المضاعفة

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

= 1 - \frac{sin ( 2 x )}{2}

1 - \frac{sin ( 2 x )}{2} = 0

انقل

1

إلى الجانب الأيمن

1 - \frac{sin ( 2 x )}{2} = 0

من الطرفين

1

اطرح

1 - \frac{sin ( 2 x )}{2} - 1 = 0 - 1

بسّط

- \frac{sin ( 2 x )}{2} = - 1

- \frac{sin ( 2 x )}{2} = - 1

2

اضرب الطرفين بـ

- \frac{sin ( 2 x )}{2} = - 1

2

اضرب الطرفين بـ

2 (- \frac{sin ( 2 x )}{2}) = 2 (- 1)

بسّط

- sin (2 x) = - 2

- sin (2 x) = - 2

- 1

اقسم الطرفين على

- sin (2 x) = - 2

- 1

اقسم الطرفين على

\frac{- sin ( 2 x )}{- 1} = \frac{- 2}{- 1}

بسّط

sin (2 x) = 2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

x \in R لا يوجد حلّ لـ

رسم

أمثلة شائعة

tan (2 θ) = 0.55

35.35=100cos(x)

35.35 = 100 cos (x)

sin (θ) = - \frac{3}{8}

sin(2x-20)=-cos(3x+50)

sin (2 x - 20) = - cos (3 x + 50)

(sin(60))/(174.36)=(sin(x))/(200)

\frac{sin ( 6 0 ^{\circ} )}{174.36} = \frac{sin ( x )}{200}