What is the general solution for 6cos(x)+1=4 ?

The general solution for 6cos(x)+1=4 is x= pi/3+2pin,x=(5pi)/3+2pin

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6cos(x)+1=4

6 cos (x) + 1 = 4

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

6 cos (x) + 1 = 4

Move

1

to the right side

6 cos (x) + 1 = 4

Subtract

1

from both sides

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

Simplify

6 cos (x) = 3

6 cos (x) = 3

Divide both sides by

6

6 cos (x) = 3

Divide both sides by

6

\frac{6 cos ( x )}{6} = \frac{3}{6}

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

sin (θ) = cos (3 7^{\circ})

cot (x) - cot (x) csc (x) = 0

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

12 cos^{2} (x) - 7 cos (x) + 1 = 0

tan (\frac{x}{2}) tan (x) = - 3

What is the general solution for 6cos(x)+1=4 ?
The general solution for 6cos(x)+1=4 is x= pi/3+2pin,x=(5pi)/3+2pin