What is the general solution for 5cos(θ)-5=0 ?

The general solution for 5cos(θ)-5=0 is θ=2pin

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5cos(θ)-5=0

5 cos (θ) - 5 = 0

θ = 2 πn

Degrees

θ = 0^{\circ} + 36 0^{\circ} n

Solution steps

5 cos (θ) - 5 = 0

Move

5

to the right side

5 cos (θ) - 5 = 0

Add

5

to both sides

5 cos (θ) - 5 + 5 = 0 + 5

Simplify

5 cos (θ) = 5

5 cos (θ) = 5

Divide both sides by

5

5 cos (θ) = 5

Divide both sides by

5

\frac{5 cos ( θ )}{5} = \frac{5}{5}

Simplify

cos (θ) = 1

cos (θ) = 1

General solutions for

cos (θ) = 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}

θ = 0 + 2 πn

θ = 0 + 2 πn

Solve

θ = 0 + 2 πn : θ = 2 πn

θ = 0 + 2 πn

0 + 2 πn = 2 πn

θ = 2 πn

θ = 2 πn

cos (2 x) - cos (x) = 1

1 - cot (x) = csc (x)

2 csc^{2} (x) = cot (x)

6 sin (x) cos (x) + 3 sin (x) - 2 cos (x) - 1 = 0

a cos (x) + b sin (x) = 0

What is the general solution for 5cos(θ)-5=0 ?
The general solution for 5cos(θ)-5=0 is θ=2pin