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Popular Trigonometry >

sin(120pit)=0.06141

Solution

sin (120 \cdot π \cdot t) = 0.06141

Solution

t = \frac{0.06144 \dots}{120 π} + \frac{n}{60}, t = \frac{1}{120} - \frac{0.06144 \dots}{120 π} + \frac{n}{60}

Degrees

t = 0.00933 \dots^{\circ} + 0.95492 \dots^{\circ} n, t = 0.46812 \dots^{\circ} + 0.95492 \dots^{\circ} n

Solution steps

sin (120 π t) = 0.06141

Apply trig inverse properties

sin (120 π t) = 0.06141

General solutions for

sin (120 π t) = 0.06141

sin (x) = a \Rightarrow x = arcsin (a) + 2 πn, x = π - arcsin (a) + 2 πn

120 π t = arcsin (0.06141) + 2 πn, 120 π t = π - arcsin (0.06141) + 2 πn

120 π t = arcsin (0.06141) + 2 πn, 120 π t = π - arcsin (0.06141) + 2 πn

Solve

120 π t = arcsin (0.06141) + 2 πn : t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

120 π t = arcsin (0.06141) + 2 πn

Divide both sides by

120 π

120 π t = arcsin (0.06141) + 2 πn

Divide both sides by

120 π

\frac{120 π t}{120 π} = \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Simplify

\frac{120 π t}{120 π} = \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Simplify

\frac{120 π t}{120 π} : t

\frac{120 π t}{120 π}

Divide the numbers:

\frac{120}{120} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π} : \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

\frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Cancel

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

Cancel

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

Cancel the common factor:

2

= \frac{πn}{60 π}

Cancel the common factor:

π

= \frac{n}{60}

= \frac{n}{60}

= \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

Solve

120 π t = π - arcsin (0.06141) + 2 πn : t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

120 π t = π - arcsin (0.06141) + 2 πn

Divide both sides by

120 π

120 π t = π - arcsin (0.06141) + 2 πn

Divide both sides by

120 π

\frac{120 π t}{120 π} = \frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Simplify

\frac{120 π t}{120 π} = \frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Simplify

\frac{120 π t}{120 π} : t

\frac{120 π t}{120 π}

Divide the numbers:

\frac{120}{120} = 1

= \frac{π t}{π}

Cancel the common factor:

π

= t

Simplify

\frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π} : \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

\frac{π}{120 π} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Cancel

\frac{π}{120 π} : \frac{1}{120}

\frac{π}{120 π}

Cancel the common factor:

π

= \frac{1}{120}

= \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{2 πn}{120 π}

Cancel

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

Cancel

\frac{2 πn}{120 π} : \frac{n}{60}

\frac{2 πn}{120 π}

Cancel the common factor:

2

= \frac{πn}{60 π}

Cancel the common factor:

π

= \frac{n}{60}

= \frac{n}{60}

= \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

t = \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}, t = \frac{1}{120} - \frac{arcsin ( 0.06141 )}{120 π} + \frac{n}{60}

Show solutions in decimal form

t = \frac{0.06144 \dots}{120 π} + \frac{n}{60}, t = \frac{1}{120} - \frac{0.06144 \dots}{120 π} + \frac{n}{60}

Graph

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sin(120*pi*t)=0.06141

Solution

Solution

Graph

Popular Examples

sin(120pit)=0.06141