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Popular >

4cos(3x-20)=1

Solution

4 cos (3 x - 20) = 1

Solution

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3} + \frac{20}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3} + \frac{20}{3}

+1

Degrees

x = 407.14602 \dots^{\circ} + 12 0^{\circ} n, x = 476.79770 \dots^{\circ} + 12 0^{\circ} n

Solution steps

4 cos (3 x - 20) = 1

Divide both sides by

4

4 cos (3 x - 20) = 1

Divide both sides by

4

\frac{4 cos ( 3 x - 20 )}{4} = \frac{1}{4}

Simplify

cos (3 x - 20) = \frac{1}{4}

cos (3 x - 20) = \frac{1}{4}

Apply trig inverse properties

cos (3 x - 20) = \frac{1}{4}

General solutions for

cos (3 x - 20) = \frac{1}{4}

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

3 x - 20 = arccos (\frac{1}{4}) + 2 πn, 3 x - 20 = 2 π - arccos (\frac{1}{4}) + 2 πn

3 x - 20 = arccos (\frac{1}{4}) + 2 πn, 3 x - 20 = 2 π - arccos (\frac{1}{4}) + 2 πn

Solve

3 x - 20 = arccos (\frac{1}{4}) + 2 πn : x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

3 x - 20 = arccos (\frac{1}{4}) + 2 πn

Move

20

to the right side

3 x - 20 = arccos (\frac{1}{4}) + 2 πn

Add

20

to both sides

3 x - 20 + 20 = arccos (\frac{1}{4}) + 2 πn + 20

Simplify

3 x = arccos (\frac{1}{4}) + 2 πn + 20

3 x = arccos (\frac{1}{4}) + 2 πn + 20

Divide both sides by

3

3 x = arccos (\frac{1}{4}) + 2 πn + 20

Divide both sides by

3

\frac{3 x}{3} = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

Simplify

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

Solve

3 x - 20 = 2 π - arccos (\frac{1}{4}) + 2 πn : x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

3 x - 20 = 2 π - arccos (\frac{1}{4}) + 2 πn

Move

20

to the right side

3 x - 20 = 2 π - arccos (\frac{1}{4}) + 2 πn

Add

20

to both sides

3 x - 20 + 20 = 2 π - arccos (\frac{1}{4}) + 2 πn + 20

Simplify

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn + 20

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn + 20

Divide both sides by

3

3 x = 2 π - arccos (\frac{1}{4}) + 2 πn + 20

Divide both sides by

3

\frac{3 x}{3} = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

Simplify

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

x = \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}, x = \frac{2 π}{3} - \frac{arccos ( \frac{1}{4} )}{3} + \frac{2 πn}{3} + \frac{20}{3}

Show solutions in decimal form

x = \frac{1.31811 \dots}{3} + \frac{2 πn}{3} + \frac{20}{3}, x = \frac{2 π}{3} - \frac{1.31811 \dots}{3} + \frac{2 πn}{3} + \frac{20}{3}

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