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Popular >

3cos(4x-26)+5=7

Solution

3 cos (4 x - 26) + 5 = 7

Solution

x = \frac{13}{2} + \frac{πn}{2} + \frac{0.84106 \dots}{4}, x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{0.84106 \dots}{4}

Degrees

x = 384.46998 \dots^{\circ} + 9 0^{\circ} n, x = 450.37514 \dots^{\circ} + 9 0^{\circ} n

Solution steps

3 cos (4 x - 26) + 5 = 7

Move

5

to the right side

3 cos (4 x - 26) + 5 = 7

Subtract

5

from both sides

3 cos (4 x - 26) + 5 - 5 = 7 - 5

Simplify

3 cos (4 x - 26) = 2

3 cos (4 x - 26) = 2

Divide both sides by

3

3 cos (4 x - 26) = 2

Divide both sides by

3

\frac{3 cos ( 4 x - 26 )}{3} = \frac{2}{3}

Simplify

cos (4 x - 26) = \frac{2}{3}

cos (4 x - 26) = \frac{2}{3}

Apply trig inverse properties

cos (4 x - 26) = \frac{2}{3}

General solutions for

cos (4 x - 26) = \frac{2}{3}

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

4 x - 26 = arccos (\frac{2}{3}) + 2 πn, 4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

4 x - 26 = arccos (\frac{2}{3}) + 2 πn, 4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

Solve

4 x - 26 = arccos (\frac{2}{3}) + 2 πn : x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

4 x - 26 = arccos (\frac{2}{3}) + 2 πn

Move

26

to the right side

4 x - 26 = arccos (\frac{2}{3}) + 2 πn

Add

26

to both sides

4 x - 26 + 26 = arccos (\frac{2}{3}) + 2 πn + 26

Simplify

4 x = arccos (\frac{2}{3}) + 2 πn + 26

4 x = arccos (\frac{2}{3}) + 2 πn + 26

Divide both sides by

4

4 x = arccos (\frac{2}{3}) + 2 πn + 26

Divide both sides by

4

\frac{4 x}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplify

\frac{4 x}{4} = \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4} : \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

\frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Group like terms

= \frac{26}{4} + \frac{2 πn}{4} + \frac{arccos ( \frac{2}{3} )}{4}

Cancel

\frac{26}{4} : \frac{13}{2}

\frac{26}{4}

Cancel the common factor:

2

= \frac{13}{2}

= \frac{13}{2} + \frac{2 πn}{4} + \frac{arccos ( \frac{2}{3} )}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}

Solve

4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn : x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

Move

26

to the right side

4 x - 26 = 2 π - arccos (\frac{2}{3}) + 2 πn

Add

26

to both sides

4 x - 26 + 26 = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

Simplify

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

Divide both sides by

4

4 x = 2 π - arccos (\frac{2}{3}) + 2 πn + 26

Divide both sides by

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplify

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Simplify

\frac{4 x}{4} : x

\frac{4 x}{4}

Divide the numbers:

\frac{4}{4} = 1

= x

Simplify

\frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4} : \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

\frac{2 π}{4} - \frac{arccos ( \frac{2}{3} )}{4} + \frac{2 πn}{4} + \frac{26}{4}

Group like terms

= \frac{2 π}{4} + \frac{26}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{2}{3} )}{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{26}{4} + \frac{2 πn}{4} - \frac{arccos ( \frac{2}{3} )}{4}

Cancel

\frac{26}{4} : \frac{13}{2}

\frac{26}{4}

Cancel the common factor:

2

= \frac{13}{2}

= \frac{π}{2} + \frac{13}{2} + \frac{2 πn}{4} - \frac{arccos ( \frac{2}{3} )}{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{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

x = \frac{13}{2} + \frac{πn}{2} + \frac{arccos ( \frac{2}{3} )}{4}, x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{arccos ( \frac{2}{3} )}{4}

Show solutions in decimal form

x = \frac{13}{2} + \frac{πn}{2} + \frac{0.84106 \dots}{4}, x = \frac{π}{2} + \frac{13}{2} + \frac{πn}{2} - \frac{0.84106 \dots}{4}

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