English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

شائع علم المثلثات >

4sin(2x-0.4)-5cos(2x-0.4)=0

الحلّ

4 sin (2 x - 0.4) - 5 cos (2 x - 0.4) = 0

الحلّ

x = \frac{1.29605 \dots}{2} + \frac{πn}{2}

درجات

x = 37.12925 \dots^{\circ} + 9 0^{\circ} n

خطوات الحلّ

4 sin (2 x - 0.4) - 5 cos (2 x - 0.4) = 0

Rewrite using trig identities

4 sin (2 x - 0.4) - 5 cos (2 x - 0.4) = 0

Rewrite using trig identities

sin (2 x - 0.4)

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

:فعّل متطابقة الطرح لزوايا

= sin (2 x) cos (0.4) - cos (2 x) sin (0.4)

sin (2 x) cos (0.4) - cos (2 x) sin (0.4)

بسّط:

0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)

sin (2 x) cos (0.4) - cos (2 x) sin (0.4)

cos (0.4)

بسّط:

0.92106 \dots

cos (0.4)

cos (0.4) = 0.92106 \dots

= 0.92106 \dots

= 0.92106 \dots sin (2 x) - sin (0.4) cos (2 x)

sin (0.4)

بسّط:

0.38941 \dots

sin (0.4)

sin (0.4) = 0.38941 \dots

= 0.38941 \dots

= 0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)

= 0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)

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

:فعّل متطابقة الطرح لزوايا

= cos (2 x) cos (0.4) + sin (2 x) sin (0.4)

cos (2 x) cos (0.4) + sin (2 x) sin (0.4)

بسّط:

0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)

cos (2 x) cos (0.4) + sin (2 x) sin (0.4)

cos (0.4)

بسّط:

0.92106 \dots

cos (0.4)

cos (0.4) = 0.92106 \dots

= 0.92106 \dots

= 0.92106 \dots cos (2 x) + sin (0.4) sin (2 x)

sin (0.4)

بسّط:

0.38941 \dots

sin (0.4)

sin (0.4) = 0.38941 \dots

= 0.38941 \dots

= 0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)

= 0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x)) = 0

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

بسّط:

1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x)) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x))

وسٌع:

3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

4 (0.92106 \dots sin (2 x) - 0.38941 \dots cos (2 x))

a (b - c) = ab - a c

: افتح أقواس بالاستعانة بـ

a = 4, b = 0.92106 \dots sin (2 x), c = 0.38941 \dots cos (2 x)

= 4 \cdot 0.92106 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

4 \cdot 0.92106 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

بسّط:

3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

4 \cdot 0.92106 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

4 \cdot 0.92106 \dots = 3.68424 \dots :

اضرب الأعداد

= 3.68424 \dots sin (2 x) - 4 \cdot 0.38941 \dots cos (2 x)

4 \cdot 0.38941 \dots = 1.55767 \dots :

اضرب الأعداد

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x)

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

- 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

وسٌع:

- 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

- 5 (0.92106 \dots cos (2 x) + 0.38941 \dots sin (2 x))

a (b + c) = ab + a c

: افتح أقواس بالاستعانة بـ

a = - 5, b = 0.92106 \dots cos (2 x), c = 0.38941 \dots sin (2 x)

= - 5 \cdot 0.92106 \dots cos (2 x) + (- 5) \cdot 0.38941 \dots sin (2 x)

فعّل قوانين سالب-موجب

+ (- a) = - a

= - 5 \cdot 0.92106 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

- 5 \cdot 0.92106 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

بسّط:

- 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

- 5 \cdot 0.92106 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

5 \cdot 0.92106 \dots = 4.60530 \dots :

اضرب الأعداد

= - 4.60530 \dots cos (2 x) - 5 \cdot 0.38941 \dots sin (2 x)

5 \cdot 0.38941 \dots = 1.94709 \dots :

اضرب الأعداد

= - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

= - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

= 3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

بسّط:

1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

3.68424 \dots sin (2 x) - 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) - 1.94709 \dots sin (2 x)

- 1.55767 \dots cos (2 x) - 4.60530 \dots cos (2 x) = - 6.16297 \dots cos (2 x) :

اجمع العناصر المتشابهة

= 3.68424 \dots sin (2 x) - 6.16297 \dots cos (2 x) - 1.94709 \dots sin (2 x)

3.68424 \dots sin (2 x) - 1.94709 \dots sin (2 x) = 1.73715 \dots sin (2 x) :

اجمع العناصر المتشابهة

= 1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

= 1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x)

1.73715 \dots sin (2 x) - 6.16297 \dots cos (2 x) = 0

cos (2 x) \neq = 0, cos (2 x)

اقسم الطرفين على

\frac{1.73715 \dots sin ( 2 x ) - 6.16297 \dots cos ( 2 x )}{cos ( 2 x )} = \frac{0}{cos ( 2 x )}

بسّط

\frac{1.73715 \dots sin ( 2 x )}{cos ( 2 x )} - 6.16297 \dots = 0

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

:Use the basic trigonometric identity

1.73715 \dots tan (2 x) - 6.16297 \dots = 0

1.73715 \dots tan (2 x) - 6.16297 \dots = 0

انقل

6.16297 \dots

إلى الجانب الأيمن

1.73715 \dots tan (2 x) - 6.16297 \dots = 0

للطرفين

6.16297 \dots

أضف

1.73715 \dots tan (2 x) - 6.16297 \dots + 6.16297 \dots = 0 + 6.16297 \dots

بسّط

1.73715 \dots tan (2 x) = 6.16297 \dots

1.73715 \dots tan (2 x) = 6.16297 \dots

1.73715 \dots

اقسم الطرفين على

1.73715 \dots tan (2 x) = 6.16297 \dots

1.73715 \dots

اقسم الطرفين على

\frac{1.73715 \dots tan ( 2 x )}{1.73715 \dots} = \frac{6.16297 \dots}{1.73715 \dots}

بسّط

tan (2 x) = 3.54774 \dots

tan (2 x) = 3.54774 \dots

Apply trig inverse properties

tan (2 x) = 3.54774 \dots

tan (2 x) = 3.54774 \dots :

حلول عامّة لـ

tan (x) = a \Rightarrow x = arctan (a) + πn

2 x = arctan (3.54774 \dots) + πn

2 x = arctan (3.54774 \dots) + πn

2 x = arctan (3.54774 \dots) + πn

حلّ:

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

2 x = arctan (3.54774 \dots) + πn

2

اقسم الطرفين على

2 x = arctan (3.54774 \dots) + πn

2

اقسم الطرفين على

\frac{2 x}{2} = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

بسّط

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

x = \frac{arctan ( 3.54774 \dots )}{2} + \frac{πn}{2}

أظهر الحلّ بالتمثيل العشريّ

x = \frac{1.29605 \dots}{2} + \frac{πn}{2}

رسم

أمثلة شائعة

cos(x)=-15/17

cos (x) = - \frac{15}{17}

sin(x)= 4/11

sin (x) = \frac{4}{11}

cos(x)=0.64

cos (x) = 0.64

solvefor x,cosh(sqrt(x))=0

so l v e f or x, cosh (x) = 0

cos(x)=0.57

cos (x) = 0.57