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Popular >

3000=5000[cos(pi/(45)(t-6))]

Solution

3000 = 5000 [cos (\frac{π}{45} (t - 6))]

Solution

t = \frac{45 \cdot 0.92729 \dots}{π} + 90 n + 6, t = 90 n + 96 - \frac{45 \cdot 0.92729 \dots}{π}

Degrees

t = 1104.80733 \dots^{\circ} + 5156.62015 \dots^{\circ} n, t = 4739.36217 \dots^{\circ} + 5156.62015 \dots^{\circ} n

Solution steps

3000 = 5000 [cos (\frac{π}{45} (t - 6))]

Switch sides

5000 [cos (\frac{π}{45} (t - 6))] = 3000

Divide both sides by

5000

5000 [cos (\frac{π}{45} (t - 6))] = 3000

Divide both sides by

5000

\frac{5000 [ cos ( \frac{π}{45} ( t - 6 ) ) ]}{5000} = \frac{3000}{5000}

Simplify

cos (\frac{π}{45} (t - 6)) = \frac{3}{5}

cos (\frac{π}{45} (t - 6)) = \frac{3}{5}

Apply trig inverse properties

cos (\frac{π}{45} (t - 6)) = \frac{3}{5}

General solutions for

cos (\frac{π}{45} (t - 6)) = \frac{3}{5}

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

\frac{π}{45} (t - 6) = arccos (\frac{3}{5}) + 2 πn, \frac{π}{45} (t - 6) = 2 π - arccos (\frac{3}{5}) + 2 πn

\frac{π}{45} (t - 6) = arccos (\frac{3}{5}) + 2 πn, \frac{π}{45} (t - 6) = 2 π - arccos (\frac{3}{5}) + 2 πn

Solve

\frac{π}{45} (t - 6) = arccos (\frac{3}{5}) + 2 πn : t = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

\frac{π}{45} (t - 6) = arccos (\frac{3}{5}) + 2 πn

Multiply both sides by

45

\frac{π}{45} (t - 6) = arccos (\frac{3}{5}) + 2 πn

Multiply both sides by

45

45 \cdot \frac{π}{45} (t - 6) = 45 arccos (\frac{3}{5}) + 45 \cdot 2 πn

Simplify

45 \cdot \frac{π}{45} (t - 6) = 45 arccos (\frac{3}{5}) + 45 \cdot 2 πn

Simplify

45 \cdot \frac{π}{45} (t - 6) : π (t - 6)

45 \cdot \frac{π}{45} (t - 6)

Multiply fractions:

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

= \frac{45 π}{45} (t - 6)

Cancel the common factor:

45

= (t - 6) π

Simplify

45 arccos (\frac{3}{5}) + 45 \cdot 2 πn : 45 arccos (\frac{3}{5}) + 90 πn

45 arccos (\frac{3}{5}) + 45 \cdot 2 πn

Multiply the numbers:

45 \cdot 2 = 90

= 45 arccos (\frac{3}{5}) + 90 πn

π (t - 6) = 45 arccos (\frac{3}{5}) + 90 πn

π (t - 6) = 45 arccos (\frac{3}{5}) + 90 πn

π (t - 6) = 45 arccos (\frac{3}{5}) + 90 πn

Divide both sides by

π

π (t - 6) = 45 arccos (\frac{3}{5}) + 90 πn

Divide both sides by

π

\frac{π ( t - 6 )}{π} = \frac{45 arccos ( \frac{3}{5} )}{π} + \frac{90 πn}{π}

Simplify

t - 6 = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

t - 6 = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

Move

6

to the right side

t - 6 = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

Add

6

to both sides

t - 6 + 6 = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

Simplify

t = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

t = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

Solve

\frac{π}{45} (t - 6) = 2 π - arccos (\frac{3}{5}) + 2 πn : t = 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

\frac{π}{45} (t - 6) = 2 π - arccos (\frac{3}{5}) + 2 πn

Multiply both sides by

45

\frac{π}{45} (t - 6) = 2 π - arccos (\frac{3}{5}) + 2 πn

Multiply both sides by

45

45 \cdot \frac{π}{45} (t - 6) = 45 \cdot 2 π - 45 arccos (\frac{3}{5}) + 45 \cdot 2 πn

Simplify

45 \cdot \frac{π}{45} (t - 6) = 45 \cdot 2 π - 45 arccos (\frac{3}{5}) + 45 \cdot 2 πn

Simplify

45 \cdot \frac{π}{45} (t - 6) : π (t - 6)

45 \cdot \frac{π}{45} (t - 6)

Multiply fractions:

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

= \frac{45 π}{45} (t - 6)

Cancel the common factor:

45

= (t - 6) π

Simplify

45 \cdot 2 π - 45 arccos (\frac{3}{5}) + 45 \cdot 2 πn : 90 π - 45 arccos (\frac{3}{5}) + 90 πn

45 \cdot 2 π - 45 arccos (\frac{3}{5}) + 45 \cdot 2 πn

Multiply the numbers:

45 \cdot 2 = 90

= 90 π - 45 arccos (\frac{3}{5}) + 90 πn

π (t - 6) = 90 π - 45 arccos (\frac{3}{5}) + 90 πn

π (t - 6) = 90 π - 45 arccos (\frac{3}{5}) + 90 πn

π (t - 6) = 90 π - 45 arccos (\frac{3}{5}) + 90 πn

Divide both sides by

π

π (t - 6) = 90 π - 45 arccos (\frac{3}{5}) + 90 πn

Divide both sides by

π

\frac{π ( t - 6 )}{π} = \frac{90 π}{π} - \frac{45 arccos ( \frac{3}{5} )}{π} + \frac{90 πn}{π}

Simplify

\frac{π ( t - 6 )}{π} = \frac{90 π}{π} - \frac{45 arccos ( \frac{3}{5} )}{π} + \frac{90 πn}{π}

Simplify

\frac{π ( t - 6 )}{π} : t - 6

\frac{π ( t - 6 )}{π}

Cancel the common factor:

π

= t - 6

Simplify

\frac{90 π}{π} - \frac{45 arccos ( \frac{3}{5} )}{π} + \frac{90 πn}{π} : 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

\frac{90 π}{π} - \frac{45 arccos ( \frac{3}{5} )}{π} + \frac{90 πn}{π}

Cancel

\frac{90 π}{π} : 90

\frac{90 π}{π}

Cancel the common factor:

π

= 90

= 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + \frac{90 πn}{π}

Cancel

\frac{90 πn}{π} : 90 n

\frac{90 πn}{π}

Cancel the common factor:

π

= 90 n

= 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

t - 6 = 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

t - 6 = 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

t - 6 = 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

Move

6

to the right side

t - 6 = 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n

Add

6

to both sides

t - 6 + 6 = 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

Simplify

t - 6 + 6 = 90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

Simplify

t - 6 + 6 : t

t - 6 + 6

Add similar elements:

- 6 + 6 = 0

= t

Simplify

90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6 : 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

90 - \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6

Add the numbers:

90 + 6 = 96

= 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

t = 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

t = 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

t = 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

t = \frac{45 arccos ( \frac{3}{5} )}{π} + 90 n + 6, t = 90 n + 96 - \frac{45 arccos ( \frac{3}{5} )}{π}

Show solutions in decimal form

t = \frac{45 \cdot 0.92729 \dots}{π} + 90 n + 6, t = 90 n + 96 - \frac{45 \cdot 0.92729 \dots}{π}

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