What is the general solution for 4cos(x)+1=3 ?

The general solution for 4cos(x)+1=3 is x= pi/3+2pin,x=(5pi)/3+2pin

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4cos(x)+1=3

4 cos (x) + 1 = 3

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Degrees

x = 6 0^{\circ} + 36 0^{\circ} n, x = 30 0^{\circ} + 36 0^{\circ} n

Solution steps

4 cos (x) + 1 = 3

Move

1

to the right side

4 cos (x) + 1 = 3

Subtract

1

from both sides

4 cos (x) + 1 - 1 = 3 - 1

Simplify

4 cos (x) = 2

4 cos (x) = 2

Divide both sides by

4

4 cos (x) = 2

Divide both sides by

4

\frac{4 cos ( x )}{4} = \frac{2}{4}

Simplify

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

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

General solutions for

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

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}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

y, x = sin (y)

sin (x) + sin (x) cos (x) = 0

tan (x) = \frac{5}{5}

sin (θ) cos (θ) = 0

csc (θ) = \frac{1}{2}

What is the general solution for 4cos(x)+1=3 ?
The general solution for 4cos(x)+1=3 is x= pi/3+2pin,x=(5pi)/3+2pin