What is the general solution for 2cos(x)-3=-5 ?

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

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2cos(x)-3=-5

2 cos (x) - 3 = - 5

x = π + 2 πn

Degrees

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

Solution steps

2 cos (x) - 3 = - 5

Move

3

to the right side

2 cos (x) - 3 = - 5

Add

3

to both sides

2 cos (x) - 3 + 3 = - 5 + 3

Simplify

2 cos (x) = - 2

2 cos (x) = - 2

Divide both sides by

2

2 cos (x) = - 2

Divide both sides by

2

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

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

sin (3 θ) - sin (θ) = cos (2 θ)

2 sin (x) + (2 - 3) = 3 csc (x)

tan^{2} (θ) + 4 sec (θ) = - 5

0 = tan (θ)

cos (θ) = \frac{4}{9}

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