What is the general solution for -2=2cos(4t) ?

The general solution for -2=2cos(4t) is t= pi/4+(pin)/2

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-2=2cos(4t)

- 2 = 2 cos (4 t)

t = \frac{π}{4} + \frac{πn}{2}

Degrees

t = 4 5^{\circ} + 9 0^{\circ} n

Solution steps

- 2 = 2 cos (4 t)

Switch sides

2 cos (4 t) = - 2

Divide both sides by

2

2 cos (4 t) = - 2

Divide both sides by

2

\frac{2 cos ( 4 t )}{2} = \frac{- 2}{2}

Simplify

cos (4 t) = - 1

cos (4 t) = - 1

General solutions for

cos (4 t) = - 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}

4 t = π + 2 πn

4 t = π + 2 πn

Solve

4 t = π + 2 πn : t = \frac{π}{4} + \frac{πn}{2}

4 t = π + 2 πn

Divide both sides by

4

4 t = π + 2 πn

Divide both sides by

4

\frac{4 t}{4} = \frac{π}{4} + \frac{2 πn}{4}

Simplify

t = \frac{π}{4} + \frac{πn}{2}

t = \frac{π}{4} + \frac{πn}{2}

t = \frac{π}{4} + \frac{πn}{2}

tan (a) = \frac{4}{5}

tan (θ) = \frac{78.48}{196.2}

sec^{2} (x) - tan (x) = 1, 0 \leq x < 2 π

4 sin^{2} (x) + 4 cos (x) = 5

cot (θ) + 1 = 0, (0, 2 π)

What is the general solution for -2=2cos(4t) ?
The general solution for -2=2cos(4t) is t= pi/4+(pin)/2