What is the general solution for solvefor x,5=4cos(3x)+9 ?

The general solution for solvefor x,5=4cos(3x)+9 is x= pi/3+(2pin)/3

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solvefor x,5=4cos(3x)+9

solve for

x, 5 = 4 cos (3 x) + 9

x = \frac{π}{3} + \frac{2 πn}{3}

Degrees

x = 6 0^{\circ} + 12 0^{\circ} n

Solution steps

5 = 4 cos (3 x) + 9

Switch sides

4 cos (3 x) + 9 = 5

Move

9

to the right side

4 cos (3 x) + 9 = 5

Subtract

9

from both sides

4 cos (3 x) + 9 - 9 = 5 - 9

Simplify

4 cos (3 x) = - 4

4 cos (3 x) = - 4

Divide both sides by

4

4 cos (3 x) = - 4

Divide both sides by

4

\frac{4 cos ( 3 x )}{4} = \frac{- 4}{4}

Simplify

cos (3 x) = - 1

cos (3 x) = - 1

General solutions for

cos (3 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}

3 x = π + 2 πn

3 x = π + 2 πn

Solve

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

3 x = π + 2 πn

Divide both sides by

3

3 x = π + 2 πn

Divide both sides by

3

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

Simplify

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

x = \frac{π}{3} + \frac{2 πn}{3}

sin^{2} (x) cos (x) + sin (x) = 0

x, 8 sec (x) + 8 tan (x) = 8

3 sin (2 x) = 5 cos^{2} (2 x)

x, y^{n} + 25 y = cos (5 x)

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

What is the general solution for solvefor x,5=4cos(3x)+9 ?
The general solution for solvefor x,5=4cos(3x)+9 is x= pi/3+(2pin)/3