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شائع علم المثلثات >

solvefor x,cos(x)(cos(x)-sin(x))=0

الحلّ

solve for

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

الحلّ

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

+1

درجات

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n, x = 4 5^{\circ} + 18 0^{\circ} n

خطوات الحلّ

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

حلّ كل جزء على حدة

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

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

cos (x) = 0 :

حلول عامّة لـ

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) - sin (x) = 0 : x = \frac{π}{4} + πn

cos (x) - sin (x) = 0

Rewrite using trig identities

cos (x) - sin (x) = 0

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

اقسم الطرفين على

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

بسّط

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

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

:Use the basic trigonometric identity

1 - tan (x) = 0

1 - tan (x) = 0

انقل

1

إلى الجانب الأيمن

1 - tan (x) = 0

من الطرفين

1

اطرح

1 - tan (x) - 1 = 0 - 1

بسّط

- tan (x) = - 1

- tan (x) = - 1

- 1

اقسم الطرفين على

- tan (x) = - 1

- 1

اقسم الطرفين على

\frac{- tan ( x )}{- 1} = \frac{- 1}{- 1}

بسّط

tan (x) = 1

tan (x) = 1

tan (x) = 1 :

حلول عامّة لـ

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

وحّد الحلول

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = \frac{π}{4} + πn

رسم

أمثلة شائعة

sin (x) = 0.72555

15=10sin(pi/(20)(x+10))+12

15 = 10 sin (\frac{π}{20} (x + 10)) + 12

-cos(x)= 2/(sqrt(20))

- cos (x) = \frac{2}{20}

tan^2(x)+7=-10sec(x),0<x<2pi

tan^{2} (x) + 7 = - 10 sec (x), 0 < x < 2 π

tan (θ) = \frac{14}{11}