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

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

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

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

x = 2 πn

Degrees

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

Solution steps

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

Move

\frac{1}{2}

to the right side

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

Add

\frac{1}{2}

to both sides

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

Simplify

\frac{cos ( x )}{2} = \frac{1}{2}

\frac{cos ( x )}{2} = \frac{1}{2}

Multiply both sides by

2

\frac{cos ( x )}{2} = \frac{1}{2}

Multiply both sides by

2

\frac{2 cos ( x )}{2} = \frac{1 \cdot 2}{2}

Simplify

\frac{2 cos ( x )}{2} = \frac{1 \cdot 2}{2}

Simplify

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

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

Divide the numbers:

\frac{2}{2} = 1

= cos (x)

Simplify

\frac{1 \cdot 2}{2} : 1

\frac{1 \cdot 2}{2}

Multiply the numbers:

1 \cdot 2 = 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

cos (x) = 1

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

tan (x) = \frac{4}{7}

sin (x) = - \frac{8}{9}

cos^{2} (θ) + 2 cos (θ) = 3

cos^{2} (x) = \frac{1}{9}

sin^{4} (x) = sin^{4} (x) cos (x)

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