ar

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

solvefor x,sin(x)+cos(y)=sin(x)cos(y)

الحلّ

solve for

x, sin (x) + cos (y) = sin (x) cos (y)

الحلّ

x = arccsc (\frac{cos ( y ) - 1}{cos ( y )}) + 2 πn, x = π + arccsc (- \frac{cos ( y ) - 1}{cos ( y )}) + 2 πn

خطوات الحلّ

sin (x) + cos (y) = sin (x) cos (y)

من الطرفين

sin (x) cos (y)

اطرح

sin (x) + cos (y) - cos (y) sin (x) = 0

Rewrite using trig identities

cos (y) + sin (x) - cos (y) sin (x)

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

:Use the basic trigonometric identity

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

cos (y) + \frac{1}{csc ( x )} - cos (y) \frac{1}{csc ( x )}

بسّط:

cos (y) + \frac{1 - cos ( y )}{csc ( x )}

cos (y) + \frac{1}{csc ( x )} - cos (y) \frac{1}{csc ( x )}

cos (y) \frac{1}{csc ( x )} = \frac{cos ( y )}{csc ( x )}

cos (y) \frac{1}{csc ( x )}

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

:اضرب كسور

= \frac{1 \cdot cos ( y )}{csc ( x )}

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

اضرب

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

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

\frac{1}{csc ( x )} - \frac{cos ( y )}{csc ( x )}

وحّد الكسور:

\frac{1 - cos ( y )}{csc ( x )}

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

فعّل القانون

= \frac{1 - cos ( y )}{csc ( x )}

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

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

cos (y) + \frac{1 - cos ( y )}{csc ( x )} = 0

csc (x)

اضرب الطرفين بـ

cos (y) + \frac{1 - cos ( y )}{csc ( x )} = 0

csc (x)

اضرب الطرفين بـ

cos (y) csc (x) + \frac{1 - cos ( y )}{csc ( x )} csc (x) = 0 \cdot csc (x)

بسّط

cos (y) csc (x) + \frac{1 - cos ( y )}{csc ( x )} csc (x) = 0 \cdot csc (x)

\frac{1 - cos ( y )}{csc ( x )} csc (x)

بسّط:

1 - cos (y)

\frac{1 - cos ( y )}{csc ( x )} csc (x)

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

:اضرب كسور

= \frac{( 1 - cos ( y ) ) csc ( x )}{csc ( x )}

csc (x) :

إلغ العوامل المشتركة

= 1 - cos (y)

0 \cdot csc (x)

بسّط:

0

0 \cdot csc (x)

0 \cdot a = 0

فعّل القانون

= 0

cos (y) csc (x) + 1 - cos (y) = 0

cos (y) csc (x) + 1 - cos (y) = 0

cos (y) csc (x) + 1 - cos (y) = 0

انقل

cos (y)

إلى الجانب الأيمن

cos (y) csc (x) + 1 - cos (y) = 0

للطرفين

cos (y)

أضف

cos (y) csc (x) + 1 - cos (y) + cos (y) = 0 + cos (y)

بسّط

cos (y) csc (x) + 1 = cos (y)

cos (y) csc (x) + 1 = cos (y)

انقل

1

إلى الجانب الأيمن

cos (y) csc (x) + 1 = cos (y)

من الطرفين

1

اطرح

cos (y) csc (x) + 1 - 1 = cos (y) - 1

بسّط

cos (y) csc (x) = cos (y) - 1

cos (y) csc (x) = cos (y) - 1

cos (y); y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

اقسم الطرفين على

cos (y) csc (x) = cos (y) - 1

cos (y); y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

اقسم الطرفين على

\frac{cos ( y ) csc ( x )}{cos ( y )} = \frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

بسّط

\frac{cos ( y ) csc ( x )}{cos ( y )} = \frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}

\frac{cos ( y ) csc ( x )}{cos ( y )}

بسّط:

csc (x)

\frac{cos ( y ) csc ( x )}{cos ( y )}

cos (y) :

إلغ العوامل المشتركة

= csc (x)

\frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}

بسّط:

\frac{cos ( y ) - 1}{cos ( y )}

\frac{cos ( y )}{cos ( y )} - \frac{1}{cos ( y )}

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

فعّل القانون

= \frac{cos ( y ) - 1}{cos ( y )}

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}; y \neq = \frac{π}{2} + 2 πn, y \neq = \frac{3 π}{2} + 2 πn

Apply trig inverse properties

csc (x) = \frac{cos ( y ) - 1}{cos ( y )}

csc (x) = \frac{cos ( y ) - 1}{cos ( y )} :

حلول عامّة لـ

csc (x) = a \Rightarrow x = arccsc (a) + 2 πn, x = π + arccsc (a) + 2 πn

x = arccsc (\frac{cos ( y ) - 1}{cos ( y )}) + 2 πn, x = π + arccsc (- \frac{cos ( y ) - 1}{cos ( y )}) + 2 πn

x = arccsc (\frac{cos ( y ) - 1}{cos ( y )}) + 2 πn, x = π + arccsc (- \frac{cos ( y ) - 1}{cos ( y )}) + 2 πn

رسم

أمثلة شائعة

solvefor x,z=arctan(x/y)

so l v e f or x, z = arctan (\frac{x}{y})

- \frac{1}{2} = cos (θ)

4cos^2(x)-3cos(x)-2=0

4 cos^{2} (x) - 3 cos (x) - 2 = 0

sin (x) = cos (3 x)

solvefor x,y=5sin(x/4)

so l v e f or x, y = 5 sin (\frac{x}{4})