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Popular >

0.06=0.1(cos(4(t)-1.57))

Solution

0.06 = 0.1 (cos (4 (t) - 1.57))

Solution

t = \frac{1.57}{4} + \frac{πn}{2} + \frac{0.92729 \dots}{4}, t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{0.92729 \dots}{4}

Degrees

t = 35.77111 \dots^{\circ} + 9 0^{\circ} n, t = 99.20606 \dots^{\circ} + 9 0^{\circ} n

Solution steps

0.06 = 0.1 (cos (4 (t) - 1.57))

Switch sides

0.1 cos (4 t - 1.57) = 0.06

Multiply both sides by

100

0.1 cos (4 t - 1.57) = 0.06

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

0.1 cos (4 t - 1.57) \cdot 100 = 0.06 \cdot 100

Refine

10 cos (4 t - 1.57) = 6

10 cos (4 t - 1.57) = 6

Divide both sides by

10

10 cos (4 t - 1.57) = 6

Divide both sides by

10

\frac{10 cos ( 4 t - 1.57 )}{10} = \frac{6}{10}

Simplify

cos (4 t - 1.57) = \frac{3}{5}

cos (4 t - 1.57) = \frac{3}{5}

Apply trig inverse properties

cos (4 t - 1.57) = \frac{3}{5}

General solutions for

cos (4 t - 1.57) = \frac{3}{5}

cos (x) = a \Rightarrow x = arccos (a) + 2 πn, x = 2 π - arccos (a) + 2 πn

4 t - 1.57 = arccos (\frac{3}{5}) + 2 πn, 4 t - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

4 t - 1.57 = arccos (\frac{3}{5}) + 2 πn, 4 t - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

Solve

4 t - 1.57 = arccos (\frac{3}{5}) + 2 πn : t = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

4 t - 1.57 = arccos (\frac{3}{5}) + 2 πn

Move

1.57

to the right side

4 t - 1.57 = arccos (\frac{3}{5}) + 2 πn

Add

1.57

to both sides

4 t - 1.57 + 1.57 = arccos (\frac{3}{5}) + 2 πn + 1.57

Simplify

4 t = arccos (\frac{3}{5}) + 2 πn + 1.57

4 t = arccos (\frac{3}{5}) + 2 πn + 1.57

Divide both sides by

4

4 t = arccos (\frac{3}{5}) + 2 πn + 1.57

Divide both sides by

4

\frac{4 t}{4} = \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplify

\frac{4 t}{4} = \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplify

\frac{4 t}{4} : t

\frac{4 t}{4}

Divide the numbers:

\frac{4}{4} = 1

= t

Simplify

\frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4} : \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

\frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Group like terms

= \frac{1.57}{4} + \frac{2 πn}{4} + \frac{arccos ( \frac{3}{5} )}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}

Solve

4 t - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn : t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

4 t - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

Move

1.57

to the right side

4 t - 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn

Add

1.57

to both sides

4 t - 1.57 + 1.57 = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

Simplify

4 t = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

4 t = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

Divide both sides by

4

4 t = 2 π - arccos (\frac{3}{5}) + 2 πn + 1.57

Divide both sides by

4

\frac{4 t}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplify

\frac{4 t}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Simplify

\frac{4 t}{4} : t

\frac{4 t}{4}

Divide the numbers:

\frac{4}{4} = 1

= t

Simplify

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4} : \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} + \frac{1.57}{4}

Group like terms

= \frac{2 π}{4} + \frac{1.57}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{3}{5} )}{4}

Cancel

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} + \frac{1.57}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{3}{5} )}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

t = \frac{1.57}{4} + \frac{πn}{2} + \frac{arccos ( \frac{3}{5} )}{4}, t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{arccos ( \frac{3}{5} )}{4}

Show solutions in decimal form

t = \frac{1.57}{4} + \frac{πn}{2} + \frac{0.92729 \dots}{4}, t = \frac{π}{2} + \frac{1.57}{4} + \frac{πn}{2} - \frac{0.92729 \dots}{4}

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