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شائع علم المثلثات >

cos(x-30)=2sin(x)

الحلّ

cos (x - 3 0^{\circ}) = 2 sin (x)

الحلّ

x = 3 0^{\circ} + 18 0^{\circ} n

راديان

x = \frac{π}{6} + πn

خطوات الحلّ

cos (x - 3 0^{\circ}) = 2 sin (x)

Rewrite using trig identities

cos (x - 3 0^{\circ}) = 2 sin (x)

Rewrite using trig identities

cos (x - 3 0^{\circ})

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

:فعّل متطابقة الطرح لزوايا

= cos (x) cos (3 0^{\circ}) + sin (x) sin (3 0^{\circ})

cos (x) cos (3 0^{\circ}) + sin (x) sin (3 0^{\circ})

بسّط:

\frac{3}{2} cos (x) + \frac{1}{2} sin (x)

cos (x) cos (3 0^{\circ}) + sin (x) sin (3 0^{\circ})

cos (3 0^{\circ})

بسّط:

\frac{3}{2}

cos (3 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

cos (3 0^{\circ}) = \frac{3}{2}

cos (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{3}{2}

= \frac{3}{2} cos (x) + sin (3 0^{\circ}) sin (x)

sin (3 0^{\circ})

بسّط:

\frac{1}{2}

sin (3 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (3 0^{\circ}) = \frac{1}{2}

sin (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

= \frac{3}{2} cos (x) + \frac{1}{2} sin (x)

\frac{3}{2} cos (x) + \frac{1}{2} sin (x) = 2 sin (x)

\frac{3}{2} cos (x) + \frac{1}{2} sin (x) = 2 sin (x)

من الطرفين

2 sin (x)

اطرح

\frac{3}{2} cos (x) - \frac{3}{2} sin (x) = 0

\frac{3}{2} cos (x) - \frac{3}{2} sin (x)

بسّط:

\frac{3 cos ( x ) - 3 sin ( x )}{2}

\frac{3}{2} cos (x) - \frac{3}{2} sin (x)

\frac{3}{2} cos (x)

اضرب بـ:

\frac{3 cos ( x )}{2}

\frac{3}{2} cos (x)

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

:اضرب كسور

= \frac{3 cos ( x )}{2}

= \frac{3 cos ( x )}{2} - \frac{3}{2} sin (x)

\frac{3}{2} sin (x)

اضرب بـ:

\frac{3 sin ( x )}{2}

\frac{3}{2} sin (x)

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

:اضرب كسور

= \frac{3 sin ( x )}{2}

= \frac{3 cos ( x )}{2} - \frac{3 sin ( x )}{2}

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

فعّل القانون

= \frac{3 cos ( x ) - 3 sin ( x )}{2}

\frac{3 cos ( x ) - 3 sin ( x )}{2} = 0

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

3 cos (x) - 3 sin (x) = 0

Rewrite using trig identities

3 cos (x) - 3 sin (x) = 0

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

اقسم الطرفين على

\frac{3 cos ( x ) - 3 sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

بسّط

3 - \frac{3 sin ( x )}{cos ( x )} = 0

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

:Use the basic trigonometric identity

3 - 3 tan (x) = 0

3 - 3 tan (x) = 0

انقل

3

إلى الجانب الأيمن

3 - 3 tan (x) = 0

من الطرفين

3

اطرح

3 - 3 tan (x) - 3 = 0 - 3

بسّط

- 3 tan (x) = - 3

- 3 tan (x) = - 3

- 3

اقسم الطرفين على

- 3 tan (x) = - 3

- 3

اقسم الطرفين على

\frac{- 3 tan ( x )}{- 3} = \frac{- 3}{- 3}

بسّط

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3}

tan (x) = \frac{3}{3} :

حلول عامّة لـ

tan (x)

periodicity table with

18 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 3 0^{\circ} + 18 0^{\circ} n

x = 3 0^{\circ} + 18 0^{\circ} n

رسم

أمثلة شائعة

sin(x)=0.04

sin (x) = 0.04

sin(x)=0.24

sin (x) = 0.24

sin(x)=0.95

sin (x) = 0.95

4-2sin(x)=0

4 - 2 sin (x) = 0

sin^2(θ)-2sin(θ)+3=0

sin^{2} (θ) - 2 sin (θ) + 3 = 0