What is the general solution for 1=cos(((pi(t-22)))/(183)) ?

The general solution for 1=cos(((pi(t-22)))/(183)) is t=366n+22

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1=cos(((pi(t-22)))/(183))

1 = cos (\frac{( π ( t - 22 ) )}{183})

t = 366 n + 22

Degrees

t = 1260.50714 \dots^{\circ} + 20970.25530 \dots^{\circ} n

Solution steps

1 = cos (\frac{( π ( t - 22 ) )}{183})

Switch sides

cos (\frac{π ( t - 22 )}{183}) = 1

General solutions for

cos (\frac{π ( t - 22 )}{183}) = 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}

\frac{π ( t - 22 )}{183} = 0 + 2 πn

\frac{π ( t - 22 )}{183} = 0 + 2 πn

Solve

\frac{π ( t - 22 )}{183} = 0 + 2 πn : t = 366 n + 22

\frac{π ( t - 22 )}{183} = 0 + 2 πn

0 + 2 πn = 2 πn

\frac{π ( t - 22 )}{183} = 2 πn

Multiply both sides by

183

\frac{π ( t - 22 )}{183} = 2 πn

Multiply both sides by

183

\frac{183 π ( t - 22 )}{183} = 183 \cdot 2 πn

Simplify

π (t - 22) = 366 πn

π (t - 22) = 366 πn

Divide both sides by

π

π (t - 22) = 366 πn

Divide both sides by

π

\frac{π ( t - 22 )}{π} = \frac{366 πn}{π}

Simplify

t - 22 = 366 n

t - 22 = 366 n

Move

22

to the right side

t - 22 = 366 n

Add

22

to both sides

t - 22 + 22 = 366 n + 22

Simplify

t = 366 n + 22

t = 366 n + 22

t = 366 n + 22

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

3 cos^{2} (θ) + 4 cos (θ) - 4 = 0

sin (x) = - cos^{2} (x) - 1

2 sin (x) cos (x) = 3 sin (x)

sin^{2} (x) = sin (2 x)

What is the general solution for 1=cos(((pi(t-22)))/(183)) ?
The general solution for 1=cos(((pi(t-22)))/(183)) is t=366n+22