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

The general solution for 2cos(x-1)=0 is x= pi/2+2pin+1,x=(3pi)/2+2pin+1

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2cos(x-1)=0

2 cos (x - 1) = 0

x = \frac{π}{2} + 2 πn + 1, x = \frac{3 π}{2} + 2 πn + 1

Degrees

x = 147.29577 \dots^{\circ} + 36 0^{\circ} n, x = 327.29577 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (x - 1) = 0

Divide both sides by

2

2 cos (x - 1) = 0

Divide both sides by

2

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

Simplify

cos (x - 1) = 0

cos (x - 1) = 0

General solutions for

cos (x - 1) = 0

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 - 1 = \frac{π}{2} + 2 πn, x - 1 = \frac{3 π}{2} + 2 πn

x - 1 = \frac{π}{2} + 2 πn, x - 1 = \frac{3 π}{2} + 2 πn

Solve

x - 1 = \frac{π}{2} + 2 πn : x = \frac{π}{2} + 2 πn + 1

x - 1 = \frac{π}{2} + 2 πn

Move

1

to the right side

x - 1 = \frac{π}{2} + 2 πn

Add

1

to both sides

x - 1 + 1 = \frac{π}{2} + 2 πn + 1

Simplify

x = \frac{π}{2} + 2 πn + 1

x = \frac{π}{2} + 2 πn + 1

Solve

x - 1 = \frac{3 π}{2} + 2 πn : x = \frac{3 π}{2} + 2 πn + 1

x - 1 = \frac{3 π}{2} + 2 πn

Move

1

to the right side

x - 1 = \frac{3 π}{2} + 2 πn

Add

1

to both sides

x - 1 + 1 = \frac{3 π}{2} + 2 πn + 1

Simplify

x = \frac{3 π}{2} + 2 πn + 1

x = \frac{3 π}{2} + 2 πn + 1

x = \frac{π}{2} + 2 πn + 1, x = \frac{3 π}{2} + 2 πn + 1

5 + 6 sin (x) = 0

sin (\frac{π}{2} x) = 0

csc (\frac{θ}{2}) = - \frac{2}{3}

x, - 2 sin (x) + 2 cos (2 x) = 0

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

What is the general solution for 2cos(x-1)=0 ?
The general solution for 2cos(x-1)=0 is x= pi/2+2pin+1,x=(3pi)/2+2pin+1