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Popular Trigonometry >

1=2sin(6.28*t)

Solution

1 = 2 sin (6.28 \cdot t)

Solution

t = \frac{25 π}{942} + \frac{50 πn}{157}, t = \frac{125 π}{942} + \frac{50 πn}{157}

Degrees

t = 4.77707 \dots^{\circ} + 57.32484 \dots^{\circ} n, t = 23.88535 \dots^{\circ} + 57.32484 \dots^{\circ} n

Solution steps

1 = 2 sin (6.28 t)

Switch sides

2 sin (6.28 t) = 1

Divide both sides by

2

2 sin (6.28 t) = 1

Divide both sides by

2

\frac{2 sin ( 6.28 t )}{2} = \frac{1}{2}

Simplify

sin (6.28 t) = \frac{1}{2}

sin (6.28 t) = \frac{1}{2}

General solutions for

sin (6.28 t) = \frac{1}{2}

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}

6.28 t = \frac{π}{6} + 2 πn, 6.28 t = \frac{5 π}{6} + 2 πn

6.28 t = \frac{π}{6} + 2 πn, 6.28 t = \frac{5 π}{6} + 2 πn

Solve

6.28 t = \frac{π}{6} + 2 πn : t = \frac{25 π}{942} + \frac{50 πn}{157}

6.28 t = \frac{π}{6} + 2 πn

Multiply both sides by

100

6.28 t = \frac{π}{6} + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

6.28 t \cdot 100 = \frac{π}{6} \cdot 100 + 2 πn \cdot 100

Refine

628 t = \frac{50 π}{3} + 200 πn

628 t = \frac{50 π}{3} + 200 πn

Divide both sides by

628

628 t = \frac{50 π}{3} + 200 πn

Divide both sides by

628

\frac{628 t}{628} = \frac{\frac{50 π}{3}}{628} + \frac{200 πn}{628}

Simplify

\frac{628 t}{628} = \frac{\frac{50 π}{3}}{628} + \frac{200 πn}{628}

Simplify

\frac{628 t}{628} : t

\frac{628 t}{628}

Divide the numbers:

\frac{628}{628} = 1

= t

Simplify

\frac{\frac{50 π}{3}}{628} + \frac{200 πn}{628} : \frac{25 π}{942} + \frac{50 πn}{157}

\frac{\frac{50 π}{3}}{628} + \frac{200 πn}{628}

\frac{\frac{50 π}{3}}{628} = \frac{25 π}{942}

\frac{\frac{50 π}{3}}{628}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{50 π}{3 \cdot 628}

Multiply the numbers:

3 \cdot 628 = 1884

= \frac{50 π}{1884}

Cancel the common factor:

2

= \frac{25 π}{942}

\frac{200 πn}{628} = \frac{50 πn}{157}

\frac{200 πn}{628}

Cancel the common factor:

4

= \frac{50 πn}{157}

= \frac{25 π}{942} + \frac{50 πn}{157}

t = \frac{25 π}{942} + \frac{50 πn}{157}

t = \frac{25 π}{942} + \frac{50 πn}{157}

t = \frac{25 π}{942} + \frac{50 πn}{157}

Solve

6.28 t = \frac{5 π}{6} + 2 πn : t = \frac{125 π}{942} + \frac{50 πn}{157}

6.28 t = \frac{5 π}{6} + 2 πn

Multiply both sides by

100

6.28 t = \frac{5 π}{6} + 2 πn

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

2

digits to the right of the decimal point, therefore multiply by

100

6.28 t \cdot 100 = \frac{5 π}{6} \cdot 100 + 2 πn \cdot 100

Refine

628 t = \frac{250 π}{3} + 200 πn

628 t = \frac{250 π}{3} + 200 πn

Divide both sides by

628

628 t = \frac{250 π}{3} + 200 πn

Divide both sides by

628

\frac{628 t}{628} = \frac{\frac{250 π}{3}}{628} + \frac{200 πn}{628}

Simplify

\frac{628 t}{628} = \frac{\frac{250 π}{3}}{628} + \frac{200 πn}{628}

Simplify

\frac{628 t}{628} : t

\frac{628 t}{628}

Divide the numbers:

\frac{628}{628} = 1

= t

Simplify

\frac{\frac{250 π}{3}}{628} + \frac{200 πn}{628} : \frac{125 π}{942} + \frac{50 πn}{157}

\frac{\frac{250 π}{3}}{628} + \frac{200 πn}{628}

\frac{\frac{250 π}{3}}{628} = \frac{125 π}{942}

\frac{\frac{250 π}{3}}{628}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{250 π}{3 \cdot 628}

Multiply the numbers:

3 \cdot 628 = 1884

= \frac{250 π}{1884}

Cancel the common factor:

2

= \frac{125 π}{942}

\frac{200 πn}{628} = \frac{50 πn}{157}

\frac{200 πn}{628}

Cancel the common factor:

4

= \frac{50 πn}{157}

= \frac{125 π}{942} + \frac{50 πn}{157}

t = \frac{125 π}{942} + \frac{50 πn}{157}

t = \frac{125 π}{942} + \frac{50 πn}{157}

t = \frac{125 π}{942} + \frac{50 πn}{157}

t = \frac{25 π}{942} + \frac{50 πn}{157}, t = \frac{125 π}{942} + \frac{50 πn}{157}

Graph

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