What is the general solution for 2cos(x)+5=4 ?

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

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2cos(x)+5=4

2 cos (x) + 5 = 4

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

Degrees

x = 12 0^{\circ} + 36 0^{\circ} n, x = 24 0^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (x) + 5 = 4

Move

5

to the right side

2 cos (x) + 5 = 4

Subtract

5

from both sides

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

Simplify

2 cos (x) = - 1

2 cos (x) = - 1

Divide both sides by

2

2 cos (x) = - 1

Divide both sides by

2

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

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{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn

cos (x) = - 0.64

y, x = tan (\frac{π}{4} y)

2 sin^{2} (x) - 5 sin (x) + 2 = 0, 0 \leq x \leq 2 π

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

sec (θ) = sin^{2} (θ) sec (θ)

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