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

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

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3-3cos(x)=3

3 - 3 cos (x) = 3

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

Degrees

x = 9 0^{\circ} + 36 0^{\circ} n, x = 27 0^{\circ} + 36 0^{\circ} n

Solution steps

3 - 3 cos (x) = 3

Subtract

3

from both sides

3 - 3 cos (x) - 3 = 3 - 3

Simplify

- 3 cos (x) = 0

Divide both sides by

- 3

- 3 cos (x) = 0

Divide both sides by

- 3

\frac{- 3 cos ( x )}{- 3} = \frac{0}{- 3}

Simplify

cos (x) = 0

cos (x) = 0

General solutions for

cos (x) = 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 = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

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

cos (x) = \frac{5}{6}, \frac{3 π}{2} \leq x \leq 2 π

tan (2 x - 3) = - 1

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

3 cos^{2} (x) + 4 cos (x) - 4 = 0

sin (θ) = - \frac{27}{190}

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