What is the general solution for cos(1000t)=1 ?

The general solution for cos(1000t)=1 is t=(pin)/(500)

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cos(1000t)=1

cos (1000 t) = 1

t = \frac{πn}{500}

Degrees

t = 0^{\circ} + 0.3 6^{\circ} n

Solution steps

cos (1000 t) = 1

General solutions for

cos (1000 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}

1000 t = 0 + 2 πn

1000 t = 0 + 2 πn

Solve

1000 t = 0 + 2 πn : t = \frac{πn}{500}

1000 t = 0 + 2 πn

0 + 2 πn = 2 πn

1000 t = 2 πn

Divide both sides by

1000

1000 t = 2 πn

Divide both sides by

1000

\frac{1000 t}{1000} = \frac{2 πn}{1000}

Simplify

t = \frac{πn}{500}

t = \frac{πn}{500}

t = \frac{πn}{500}

3 sin (\frac{θ}{4}) - \frac{3}{2} = 0, 0 \leq θ \leq 2 π

\frac{1 - tan ^{2} ( A )}{2 tan ( A )} = cot (A)

cos (4 θ) = cos (2 θ), 18 0^{\circ} \leq θ \leq 36 0^{\circ}

2 sin (x) = cos (x)

8 cos (2 x) = 8 - 8 cos (2 x)

What is the general solution for cos(1000t)=1 ?
The general solution for cos(1000t)=1 is t=(pin)/(500)