What is the general solution for 5sin(60t)=0 ?

The general solution for 5sin(60t)=0 is t=(pin)/(30),t= pi/(60)+(pin)/(30)

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5sin(60t)=0

5 sin (60 t) = 0

t = \frac{πn}{30}, t = \frac{π}{60} + \frac{πn}{30}

Degrees

t = 0^{\circ} + 6^{\circ} n, t = 3^{\circ} + 6^{\circ} n

Solution steps

5 sin (60 t) = 0

Divide both sides by

5

5 sin (60 t) = 0

Divide both sides by

5

\frac{5 sin ( 60 t )}{5} = \frac{0}{5}

Simplify

sin (60 t) = 0

sin (60 t) = 0

General solutions for

sin (60 t) = 0

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

60 t = 0 + 2 πn, 60 t = π + 2 πn

60 t = 0 + 2 πn, 60 t = π + 2 πn

Solve

60 t = 0 + 2 πn : t = \frac{πn}{30}

60 t = 0 + 2 πn

0 + 2 πn = 2 πn

60 t = 2 πn

Divide both sides by

60

60 t = 2 πn

Divide both sides by

60

\frac{60 t}{60} = \frac{2 πn}{60}

Simplify

t = \frac{πn}{30}

t = \frac{πn}{30}

Solve

60 t = π + 2 πn : t = \frac{π}{60} + \frac{πn}{30}

60 t = π + 2 πn

Divide both sides by

60

60 t = π + 2 πn

Divide both sides by

60

\frac{60 t}{60} = \frac{π}{60} + \frac{2 πn}{60}

Simplify

t = \frac{π}{60} + \frac{πn}{30}

t = \frac{π}{60} + \frac{πn}{30}

t = \frac{πn}{30}, t = \frac{π}{60} + \frac{πn}{30}

18 sin^{2} (x) + 3 cos (x) - 17 = 0

sin (2 θ) = 0.4905

tan (θ) = \frac{- 4.86}{14.56}

12 cos (x) + 5 sin (x) = 3

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

What is the general solution for 5sin(60t)=0 ?
The general solution for 5sin(60t)=0 is t=(pin)/(30),t= pi/(60)+(pin)/(30)