What is the general solution for cos(4x)=0.8-0.6 ?

The general solution for cos(4x)=0.8-0.6 is x=(1.36943…)/4+(pin)/2 ,x= pi/2-(1.36943…)/4+(pin)/2

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cos(4x)=0.8-0.6

cos (4 x) = 0.8 - 0.6

x = \frac{1.36943 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.36943 \dots}{4} + \frac{πn}{2}

Degrees

x = 19.61576 \dots^{\circ} + 9 0^{\circ} n, x = 70.38423 \dots^{\circ} + 9 0^{\circ} n

Solution steps

cos (4 x) = 0.8 - 0.6

Subtract the numbers:

0.8 - 0.6 = 0.2

cos (4 x) = 0.2

Apply trig inverse properties

cos (4 x) = 0.2

General solutions for

cos (4 x) = 0.2

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

4 x = arccos (0.2) + 2 πn, 4 x = 2 π - arccos (0.2) + 2 πn

4 x = arccos (0.2) + 2 πn, 4 x = 2 π - arccos (0.2) + 2 πn

Solve

4 x = arccos (0.2) + 2 πn : x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

4 x = arccos (0.2) + 2 πn

Divide both sides by

4

4 x = arccos (0.2) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{4}

Simplify

x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

Solve

4 x = 2 π - arccos (0.2) + 2 πn : x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

4 x = 2 π - arccos (0.2) + 2 πn

Divide both sides by

4

4 x = 2 π - arccos (0.2) + 2 πn

Divide both sides by

4

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( 0.2 )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 x}{4} = \frac{2 π}{4} - \frac{arccos ( 0.2 )}{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 ( 0.2 )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( 0.2 )}{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 ( 0.2 )}{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 ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

x = \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{arccos ( 0.2 )}{4} + \frac{πn}{2}

Show solutions in decimal form

x = \frac{1.36943 \dots}{4} + \frac{πn}{2}, x = \frac{π}{2} - \frac{1.36943 \dots}{4} + \frac{πn}{2}

5 cos^{2} (x) = 4 - 3 sin^{2} (x)

\frac{18 cos ( 2 θ ) + 2 + cos ( θ )}{2} = 0

0 = 3 sin (x - \frac{1}{2} π) + 2

2 sin^{2} (x) = 3 sin (x)

5 + 2 sin (x) - 7 = 0

What is the general solution for cos(4x)=0.8-0.6 ?
The general solution for cos(4x)=0.8-0.6 is x=(1.36943…)/4+(pin)/2 ,x= pi/2-(1.36943…)/4+(pin)/2