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Popular Trigonometry >

1.5=2.75cos(30(x-4))+3.25

Solution

1.5 = 2.75 cos (30 (x - 4)) + 3.25

Solution

x = \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4, x = - \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4

Degrees

x = 233.50049 \dots^{\circ} + 1 2^{\circ} n, x = 224.86574 \dots^{\circ} + 1 2^{\circ} n

Solution steps

1.5 = 2.75 cos (30 (x - 4)) + 3.25

Switch sides

2.75 cos (30 (x - 4)) + 3.25 = 1.5

Multiply both sides by

100

2.75 cos (30 (x - 4)) + 3.25 = 1.5

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

2.75 cos (30 (x - 4)) \cdot 100 + 3.25 \cdot 100 = 1.5 \cdot 100

Refine

275 cos (30 (x - 4)) + 325 = 150

275 cos (30 (x - 4)) + 325 = 150

Move

325

to the right side

275 cos (30 (x - 4)) + 325 = 150

Subtract

325

from both sides

275 cos (30 (x - 4)) + 325 - 325 = 150 - 325

Simplify

275 cos (30 (x - 4)) = - 175

275 cos (30 (x - 4)) = - 175

Divide both sides by

275

275 cos (30 (x - 4)) = - 175

Divide both sides by

275

\frac{275 cos ( 30 ( x - 4 ) )}{275} = \frac{- 175}{275}

Simplify

\frac{275 cos ( 30 ( x - 4 ) )}{275} = \frac{- 175}{275}

Simplify

\frac{275 cos ( 30 ( x - 4 ) )}{275} : cos (30 (x - 4))

\frac{275 cos ( 30 ( x - 4 ) )}{275}

Divide the numbers:

\frac{275}{275} = 1

= cos (30 (x - 4))

Simplify

\frac{- 175}{275} : - \frac{7}{11}

\frac{- 175}{275}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{175}{275}

Cancel the common factor:

25

= - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

cos (30 (x - 4)) = - \frac{7}{11}

Apply trig inverse properties

cos (30 (x - 4)) = - \frac{7}{11}

General solutions for

cos (30 (x - 4)) = - \frac{7}{11}

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

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn, 30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn, 30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

Solve

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn : x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn

Divide both sides by

30

30 (x - 4) = arccos (- \frac{7}{11}) + 2 πn

Divide both sides by

30

\frac{30 ( x - 4 )}{30} = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{2 πn}{30}

Simplify

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Move

4

to the right side

x - 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Add

4

to both sides

x - 4 + 4 = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Simplify

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Solve

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn : x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

Divide both sides by

30

30 (x - 4) = - arccos (- \frac{7}{11}) + 2 πn

Divide both sides by

30

\frac{30 ( x - 4 )}{30} = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{2 πn}{30}

Simplify

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Move

4

to the right side

x - 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15}

Add

4

to both sides

x - 4 + 4 = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Simplify

x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

x = \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4, x = - \frac{arccos ( - \frac{7}{11} )}{30} + \frac{πn}{15} + 4

Show solutions in decimal form

x = \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4, x = - \frac{2.26057 \dots}{30} + \frac{πn}{15} + 4

Graph

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