What is the general solution for 6=6sin(2pi(47)t),0<t<0.0212 ?

Q: What is the general solution for 6=6sin(2pi(47)t),0<t<0.0212 ?

The general solution for 6=6sin(2pi(47)t),0<t<0.0212 is t= 1/188

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Popular Trigonometry >

6=6sin(2pi(47)t),0<t<0.0212

Solution

6 = 6 sin (2 π (47) t), 0 < t < 0.0212

Solution

t = \frac{1}{188}

Degrees

t = 0.30476 \dots^{\circ}

Solution steps

6 = 6 sin (2 π (47) t), 0 < t < 0.0212

Switch sides

6 sin (2 π 47 t) = 6

Divide both sides by

6

6 sin (2 π 47 t) = 6

Divide both sides by

6

\frac{6 sin ( 2 π 47 t )}{6} = \frac{6}{6}

Simplify

sin (2 π 47 t) = 1

sin (2 π 47 t) = 1

General solutions for

sin (2 π 47 t) = 1

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}

2 π 47 t = \frac{π}{2} + 2 πn

2 π 47 t = \frac{π}{2} + 2 πn

Solve

2 π 47 t = \frac{π}{2} + 2 πn : t = \frac{1}{188} + \frac{n}{47}

2 π 47 t = \frac{π}{2} + 2 πn

Divide both sides by

94 π

2 π 47 t = \frac{π}{2} + 2 πn

Divide both sides by

94 π

\frac{2 π 47 t}{94 π} = \frac{\frac{π}{2}}{94 π} + \frac{2 πn}{94 π}

Simplify

\frac{2 π 47 t}{94 π} = \frac{\frac{π}{2}}{94 π} + \frac{2 πn}{94 π}

Simplify

\frac{2 π 47 t}{94 π} : t

\frac{2 π 47 t}{94 π}

Multiply the numbers:

2 \cdot 47 = 94

= \frac{94 π t}{94 π}

Divide the numbers:

\frac{94}{94} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{\frac{π}{2}}{94 π} + \frac{2 πn}{94 π} : \frac{1}{188} + \frac{n}{47}

\frac{\frac{π}{2}}{94 π} + \frac{2 πn}{94 π}

\frac{\frac{π}{2}}{94 π} = \frac{1}{188}

\frac{\frac{π}{2}}{94 π}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 94 π}

Multiply the numbers:

2 \cdot 94 = 188

= \frac{π}{188 π}

Cancel the common factor:

π

= \frac{1}{188}

\frac{2 πn}{94 π} = \frac{n}{47}

\frac{2 πn}{94 π}

Cancel

\frac{2 πn}{94 π} : \frac{n}{47}

\frac{2 πn}{94 π}

Cancel the common factor:

2

= \frac{πn}{47 π}

Cancel the common factor:

π

= \frac{n}{47}

= \frac{n}{47}

= \frac{1}{188} + \frac{n}{47}

t = \frac{1}{188} + \frac{n}{47}

t = \frac{1}{188} + \frac{n}{47}

t = \frac{1}{188} + \frac{n}{47}

t = \frac{1}{188} + \frac{n}{47}

Solutions for the range

0 < t < 0.0212

t = \frac{1}{188}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 6=6sin(2pi(47)t),0<t<0.0212 ?
The general solution for 6=6sin(2pi(47)t),0<t<0.0212 is t= 1/188