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sin^2(x)=1,0<= x<= 2pi

الحلّ

sin^{2} (x) = 1, 0 \leq x \leq 2 π

الحلّ

x = \frac{π}{2}, x = \frac{3 π}{2}

+1

درجات

x = 9 0^{\circ}, x = 27 0^{\circ}

خطوات الحلّ

sin^{2} (x) = 1, 0 \leq x \leq 2 π

بالاستعانة بطريقة التعويض

sin^{2} (x) = 1

sin (x) = u :

على افتراض أنّ

u^{2} = 1

u^{2} = 1 : u = 1, u = - 1

u^{2} = 1

x = f (a), - f (a)

الحلول هي

x^{2} = f (a)

لـ

u = 1, u = - 1

1 = 1

1

1 = 1

فعّل القانون

= 1

- 1 = - 1

- 1

1 = 1

فعّل القانون

= - 1

u = 1, u = - 1

u = sin (x)

استبدل مجددًا

sin (x) = 1, sin (x) = - 1

sin (x) = 1, sin (x) = - 1

sin (x) = 1, 0 \leq x \leq 2 π : x = \frac{π}{2}

sin (x) = 1, 0 \leq x \leq 2 π

sin (x) = 1 :

حلول عامّة لـ

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{π}{2} + 2 πn

x = \frac{π}{2} + 2 πn

0 \leq x \leq 2 π :

حلول للمدى

x = \frac{π}{2}

sin (x) = - 1, 0 \leq x \leq 2 π : x = \frac{3 π}{2}

sin (x) = - 1, 0 \leq x \leq 2 π

sin (x) = - 1 :

حلول عامّة لـ

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = \frac{3 π}{2} + 2 πn

x = \frac{3 π}{2} + 2 πn

0 \leq x \leq 2 π :

حلول للمدى

x = \frac{3 π}{2}

وحّد الحلول

x = \frac{π}{2}, x = \frac{3 π}{2}

أمثلة شائعة

tan(x)sin^2(x)=tan(x)

tan (x) sin^{2} (x) = tan (x)

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

tan (θ) = 5

2sin^2(θ)-sin(θ)=0

2 sin^{2} (θ) - sin (θ) = 0

sec^2(x)+tan(x)=3

sec^{2} (x) + tan (x) = 3