What is the general solution for 4cos(x)+3=5 ?

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

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4cos(x)+3=5

4 cos (x) + 3 = 5

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) + 3 = 5

Move

3

to the right side

4 cos (x) + 3 = 5

Subtract

3

from both sides

4 cos (x) + 3 - 3 = 5 - 3

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

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