What is the general solution for cos(2x+15)=0.3 ?

The general solution for cos(2x+15)=0.3 is x=pin-15/2+(1.26610…)/2 ,x=pi+pin-15/2-(1.26610…)/2

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cos(2x+15)=0.3

Solution

cos (2 x + 15) = 0.3

Solution

x = πn - \frac{15}{2} + \frac{1.26610 \dots}{2}, x = π + πn - \frac{15}{2} - \frac{1.26610 \dots}{2}

Degrees

x = - 393.44714 \dots^{\circ} + 18 0^{\circ} n, x = - 285.98954 \dots^{\circ} + 18 0^{\circ} n

Solution steps

cos (2 x + 15) = 0.3

Apply trig inverse properties

cos (2 x + 15) = 0.3

General solutions for

cos (2 x + 15) = 0.3

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

2 x + 15 = arccos (0.3) + 2 πn, 2 x + 15 = 2 π - arccos (0.3) + 2 πn

2 x + 15 = arccos (0.3) + 2 πn, 2 x + 15 = 2 π - arccos (0.3) + 2 πn

Solve

2 x + 15 = arccos (0.3) + 2 πn : x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

2 x + 15 = arccos (0.3) + 2 πn

Move

15

to the right side

2 x + 15 = arccos (0.3) + 2 πn

Subtract

15

from both sides

2 x + 15 - 15 = arccos (0.3) + 2 πn - 15

Simplify

2 x = arccos (0.3) + 2 πn - 15

2 x = arccos (0.3) + 2 πn - 15

Divide both sides by

2

2 x = arccos (0.3) + 2 πn - 15

Divide both sides by

2

\frac{2 x}{2} = \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} = \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2} : πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

\frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Group like terms

= - \frac{15}{2} + \frac{2 πn}{2} + \frac{arccos ( 0.3 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= - \frac{15}{2} + πn + \frac{arccos ( 0.3 )}{2}

Group like terms

= πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}

Solve

2 x + 15 = 2 π - arccos (0.3) + 2 πn : x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

2 x + 15 = 2 π - arccos (0.3) + 2 πn

Move

15

to the right side

2 x + 15 = 2 π - arccos (0.3) + 2 πn

Subtract

15

from both sides

2 x + 15 - 15 = 2 π - arccos (0.3) + 2 πn - 15

Simplify

2 x = 2 π - arccos (0.3) + 2 πn - 15

2 x = 2 π - arccos (0.3) + 2 πn - 15

Divide both sides by

2

2 x = 2 π - arccos (0.3) + 2 πn - 15

Divide both sides by

2

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} = \frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

\frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2} : π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

\frac{2 π}{2} - \frac{arccos ( 0.3 )}{2} + \frac{2 πn}{2} - \frac{15}{2}

Group like terms

= \frac{2 π}{2} - \frac{15}{2} + \frac{2 πn}{2} - \frac{arccos ( 0.3 )}{2}

Divide the numbers:

\frac{2}{2} = 1

= π - \frac{15}{2} + πn - \frac{arccos ( 0.3 )}{2}

Group like terms

= π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

x = πn - \frac{15}{2} + \frac{arccos ( 0.3 )}{2}, x = π + πn - \frac{15}{2} - \frac{arccos ( 0.3 )}{2}

Show solutions in decimal form

x = πn - \frac{15}{2} + \frac{1.26610 \dots}{2}, x = π + πn - \frac{15}{2} - \frac{1.26610 \dots}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for cos(2x+15)=0.3 ?
The general solution for cos(2x+15)=0.3 is x=pin-15/2+(1.26610…)/2 ,x=pi+pin-15/2-(1.26610…)/2