What is the general solution for (1-cos(x))(2-sin(x))=0 ?

The general solution for (1-cos(x))(2-sin(x))=0 is x=2pin

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Popular >

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

Solution

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

Solution

x = 2 πn

Degrees

x = 0^{\circ} + 36 0^{\circ} n

Solution steps

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

Solving each part separately

1 - cos (x) = 0 or 2 - sin (x) = 0

1 - cos (x) = 0 : x = 2 πn

1 - cos (x) = 0

Move

1

to the right side

1 - cos (x) = 0

Subtract

1

from both sides

1 - cos (x) - 1 = 0 - 1

Simplify

- cos (x) = - 1

- cos (x) = - 1

Divide both sides by

- 1

- cos (x) = - 1

Divide both sides by

- 1

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

Simplify

cos (x) = 1

cos (x) = 1

General solutions for

cos (x) = 1

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 = 0 + 2 πn

x = 0 + 2 πn

Solve

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn

2 - sin (x) = 0 :

No Solution

2 - sin (x) = 0

Move

2

to the right side

2 - sin (x) = 0

Subtract

2

from both sides

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

Simplify

- sin (x) = - 2

- sin (x) = - 2

Divide both sides by

- 1

- sin (x) = - 2

Divide both sides by

- 1

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

Simplify

sin (x) = 2

sin (x) = 2

- 1 \leq sin (x) \leq 1

No Solution

Combine all the solutions

x = 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for (1-cos(x))(2-sin(x))=0 ?
The general solution for (1-cos(x))(2-sin(x))=0 is x=2pin