en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(4θ+20)=0.8

Solution

2 cos (4 θ + 20) = 0.8

Solution

θ = - 5 + \frac{πn}{2} + \frac{1.15927 \dots}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{1.15927 \dots}{4} - 5

+1

Degrees

θ = - 269.87344 \dots^{\circ} + 9 0^{\circ} n, θ = - 213.08435 \dots^{\circ} + 9 0^{\circ} n

Solution steps

2 cos (4 θ + 20) = 0.8

Divide both sides by

2

2 cos (4 θ + 20) = 0.8

Divide both sides by

2

\frac{2 cos ( 4 θ + 20 )}{2} = \frac{0.8}{2}

Simplify

cos (4 θ + 20) = 0.4

cos (4 θ + 20) = 0.4

Apply trig inverse properties

cos (4 θ + 20) = 0.4

General solutions for

cos (4 θ + 20) = 0.4

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

4 θ + 20 = arccos (0.4) + 2 πn, 4 θ + 20 = 2 π - arccos (0.4) + 2 πn

4 θ + 20 = arccos (0.4) + 2 πn, 4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Solve

4 θ + 20 = arccos (0.4) + 2 πn : θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

4 θ + 20 = arccos (0.4) + 2 πn

Move

20

to the right side

4 θ + 20 = arccos (0.4) + 2 πn

Subtract

20

from both sides

4 θ + 20 - 20 = arccos (0.4) + 2 πn - 20

Simplify

4 θ = arccos (0.4) + 2 πn - 20

4 θ = arccos (0.4) + 2 πn - 20

Divide both sides by

4

4 θ = arccos (0.4) + 2 πn - 20

Divide both sides by

4

\frac{4 θ}{4} = \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplify

\frac{4 θ}{4} = \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4} : - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

\frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Group like terms

= - \frac{20}{4} + \frac{2 πn}{4} + \frac{arccos ( 0.4 )}{4}

Divide the numbers:

\frac{20}{4} = 5

= - 5 + \frac{2 πn}{4} + \frac{arccos ( 0.4 )}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

Solve

4 θ + 20 = 2 π - arccos (0.4) + 2 πn : θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Move

20

to the right side

4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Subtract

20

from both sides

4 θ + 20 - 20 = 2 π - arccos (0.4) + 2 πn - 20

Simplify

4 θ = 2 π - arccos (0.4) + 2 πn - 20

4 θ = 2 π - arccos (0.4) + 2 πn - 20

Divide both sides by

4

4 θ = 2 π - arccos (0.4) + 2 πn - 20

Divide both sides by

4

\frac{4 θ}{4} = \frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplify

\frac{4 θ}{4} = \frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Simplify

\frac{4 θ}{4} : θ

\frac{4 θ}{4}

Divide the numbers:

\frac{4}{4} = 1

= θ

Simplify

\frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4} : \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

\frac{2 π}{4} - \frac{arccos ( 0.4 )}{4} + \frac{2 πn}{4} - \frac{20}{4}

Group like terms

= \frac{2 π}{4} - \frac{20}{4} + \frac{2 πn}{4} - \frac{arccos ( 0.4 )}{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{20}{4} + \frac{2 πn}{4} - \frac{arccos ( 0.4 )}{4}

Divide the numbers:

\frac{20}{4} = 5

= \frac{π}{2} - 5 + \frac{2 πn}{4} - \frac{arccos ( 0.4 )}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{2} - 5 + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4}

Group like terms

= \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

Show solutions in decimal form

θ = - 5 + \frac{πn}{2} + \frac{1.15927 \dots}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{1.15927 \dots}{4} - 5

Popular Examples

2-2cos^2(x/2)=sin^2(x)

2 - 2 cos^{2} (\frac{x}{2}) = sin^{2} (x)

sin(θ)=(sqrt(2))/2 ,0<= θ<= 2pi

sin (θ) = \frac{2}{2}, 0 \leq θ \leq 2 π

solvefor x,cos(x)= 2/3 solve for

x, cos (x) = \frac{2}{3}

3 sin (x) + 2 = 1.5

3sec^2(x)-2tan(x)-4=0

3 sec^{2} (x) - 2 tan (x) - 4 = 0