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شائع علم المثلثات >

cos(x+90)=sin(x)+1

الحلّ

cos (x + 9 0^{\circ}) = sin (x) + 1

الحلّ

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

راديان

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

خطوات الحلّ

cos (x + 9 0^{\circ}) = sin (x) + 1

Rewrite using trig identities

cos (x + 9 0^{\circ}) = sin (x) + 1

Rewrite using trig identities

cos (x + 9 0^{\circ})

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

:فعّل متطابقة الجمع لزوايا

= cos (x) cos (9 0^{\circ}) - sin (x) sin (9 0^{\circ})

cos (x) cos (9 0^{\circ}) - sin (x) sin (9 0^{\circ})

بسّط:

- sin (x)

cos (x) cos (9 0^{\circ}) - sin (x) sin (9 0^{\circ})

cos (x) cos (9 0^{\circ}) = 0

cos (x) cos (9 0^{\circ})

cos (9 0^{\circ})

بسّط:

0

cos (9 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

cos (9 0^{\circ}) = 0

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}

= 0

= 0 \cdot cos (x)

0 \cdot a = 0

فعّل القانون

= 0

sin (x) sin (9 0^{\circ}) = sin (x)

sin (x) sin (9 0^{\circ})

sin (9 0^{\circ})

بسّط:

1

sin (9 0^{\circ})

استخدم المتطابقة الأساسيّة التالية:

sin (9 0^{\circ}) = 1

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}

= 1

= 1 \cdot sin (x)

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

اضرب

= sin (x)

= 0 - sin (x)

0 - sin (x) = - sin (x)

= - sin (x)

= - sin (x)

- sin (x) = sin (x) + 1

- sin (x) = sin (x) + 1

من الطرفين

sin (x) + 1

اطرح

- 2 sin (x) - 1 = 0

انقل

1

إلى الجانب الأيمن

- 2 sin (x) - 1 = 0

للطرفين

1

أضف

- 2 sin (x) - 1 + 1 = 0 + 1

بسّط

- 2 sin (x) = 1

- 2 sin (x) = 1

- 2

اقسم الطرفين على

- 2 sin (x) = 1

- 2

اقسم الطرفين على

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

بسّط

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

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

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

حلول عامّة لـ

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}

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

x = 21 0^{\circ} + 36 0^{\circ} n, x = 33 0^{\circ} + 36 0^{\circ} n

رسم

أمثلة شائعة

7sec(x)-11=0

7 sec (x) - 11 = 0

sin(x)+(sqrt(3))/2 =0

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

cos(2θ)+cos(θ)+1=0

cos (2 θ) + cos (θ) + 1 = 0

3cos^2(x)-5cos(x)-2=0

3 cos^{2} (x) - 5 cos (x) - 2 = 0

cos(2x)+1=-2cos(x)

cos (2 x) + 1 = - 2 cos (x)