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Popular >

4.1=4.2cos(18t)+3

Solution

4.1 = 4.2 cos (18 t) + 3

Solution

t = \frac{1.30580 \dots}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{1.30580 \dots}{18} + \frac{πn}{9}

Degrees

t = 4.15649 \dots^{\circ} + 2 0^{\circ} n, t = 15.84350 \dots^{\circ} + 2 0^{\circ} n

Solution steps

4.1 = 4.2 cos (18 t) + 3

Switch sides

4.2 cos (18 t) + 3 = 4.1

Multiply both sides by

10

4.2 cos (18 t) + 3 = 4.1

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere is one digit to the right of the decimal point, therefore multiply by

10

4.2 cos (18 t) \cdot 10 + 3 \cdot 10 = 4.1 \cdot 10

Refine

42 cos (18 t) + 30 = 41

42 cos (18 t) + 30 = 41

Move

30

to the right side

42 cos (18 t) + 30 = 41

Subtract

30

from both sides

42 cos (18 t) + 30 - 30 = 41 - 30

Simplify

42 cos (18 t) = 11

42 cos (18 t) = 11

Divide both sides by

42

42 cos (18 t) = 11

Divide both sides by

42

\frac{42 cos ( 18 t )}{42} = \frac{11}{42}

Simplify

cos (18 t) = \frac{11}{42}

cos (18 t) = \frac{11}{42}

Apply trig inverse properties

cos (18 t) = \frac{11}{42}

General solutions for

cos (18 t) = \frac{11}{42}

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

18 t = arccos (\frac{11}{42}) + 2 πn, 18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

18 t = arccos (\frac{11}{42}) + 2 πn, 18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

Solve

18 t = arccos (\frac{11}{42}) + 2 πn : t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

18 t = arccos (\frac{11}{42}) + 2 πn

Divide both sides by

18

18 t = arccos (\frac{11}{42}) + 2 πn

Divide both sides by

18

\frac{18 t}{18} = \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

Simplify

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

Solve

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn : t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

Divide both sides by

18

18 t = 2 π - arccos (\frac{11}{42}) + 2 πn

Divide both sides by

18

\frac{18 t}{18} = \frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

Simplify

\frac{18 t}{18} = \frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

Simplify

\frac{18 t}{18} : t

\frac{18 t}{18}

Divide the numbers:

\frac{18}{18} = 1

= t

Simplify

\frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18} : \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

\frac{2 π}{18} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

Cancel

\frac{2 π}{18} : \frac{π}{9}

\frac{2 π}{18}

Cancel the common factor:

2

= \frac{π}{9}

= \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{2 πn}{18}

Cancel

\frac{2 πn}{18} : \frac{πn}{9}

\frac{2 πn}{18}

Cancel the common factor:

2

= \frac{πn}{9}

= \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

t = \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{arccos ( \frac{11}{42} )}{18} + \frac{πn}{9}

Show solutions in decimal form

t = \frac{1.30580 \dots}{18} + \frac{πn}{9}, t = \frac{π}{9} - \frac{1.30580 \dots}{18} + \frac{πn}{9}

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