What is the general solution for 0.6=cos(4x) ?

The general solution for 0.6=cos(4x) is x=(0.92729…)/4+(pin)/2 ,x= pi/2-(0.92729…)/4+(pin)/2

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0.6=cos(4x)

0.6 = cos (4 x)

x = \frac{0.92729 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.92729 \dots}{4} + \frac{πn}{2}

Degrees

x = 13.28252 \dots^{\circ} + 9 0^{\circ} n, x = 76.71747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

0.6 = cos (4 x)

Switch sides

cos (4 x) = 0.6

Apply trig inverse properties

cos (4 x) = 0.6

General solutions for

cos (4 x) = 0.6

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

4 x = arccos (0.6) + 2 πn, 4 x = 2 π - arccos (0.6) + 2 πn

4 x = arccos (0.6) + 2 πn, 4 x = 2 π - arccos (0.6) + 2 πn

Solve

4 x = arccos (0.6) + 2 πn : x = \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

4 x = arccos (0.6) + 2 πn

Divide both sides by

4

4 x = arccos (0.6) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arccos ( 0.6 )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

x = \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

Solve

4 x = 2 π - arccos (0.6) + 2 πn : x = \frac{π}{2} - \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

4 x = 2 π - arccos (0.6) + 2 πn

Divide both sides by

4

4 x = 2 π - arccos (0.6) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( 0.6 )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( 0.6 )}{4} + \frac{2 πn}{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 ( 0.6 )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( 0.6 )}{4} + \frac{2 πn}{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{arccos ( 0.6 )}{4} + \frac{2 πn}{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{arccos ( 0.6 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

x = \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( 0.6 )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{0.92729 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{0.92729 \dots}{4} + \frac{πn}{2}

sin (x) = \frac{1}{1.33}

- 3 = cos (0 + C)

cos (θ) + 3 sin (\frac{θ}{2}) - 2 = 0

2 sec (θ) = 6

sin (2 x + 20) - 1 = \frac{- 1}{2}

What is the general solution for 0.6=cos(4x) ?
The general solution for 0.6=cos(4x) is x=(0.92729…)/4+(pin)/2 ,x= pi/2-(0.92729…)/4+(pin)/2