What is the general solution for 3cos(x)+3=0 ?

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

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3cos(x)+3=0

3 cos (x) + 3 = 0

x = π + 2 πn

Degrees

x = 18 0^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (x) + 3 = 0

Move

3

to the right side

3 cos (x) + 3 = 0

Subtract

3

from both sides

3 cos (x) + 3 - 3 = 0 - 3

Simplify

3 cos (x) = - 3

3 cos (x) = - 3

Divide both sides by

3

3 cos (x) = - 3

Divide both sides by

3

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

Simplify

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 = π + 2 πn

x = π + 2 πn

- 2 cos^{2} (x) + 3 cos (x) - 1 = 0

2 cos (2 x) - 3 cos (x) = 0

sin (2 x) = \frac{3}{5}

- cos (x) = sin (x)

2 cos^{2} (x) + 5 cos (x) - 3 = 0

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