What is the general solution for 2cos(x)=-0.2 ?

The general solution for 2cos(x)=-0.2 is x=1.67096…+2pin,x=-1.67096…+2pin

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2cos(x)=-0.2

2 cos (x) = - 0.2

x = 1.67096 \dots + 2 πn, x = - 1.67096 \dots + 2 πn

Degrees

x = 95.73917 \dots^{\circ} + 36 0^{\circ} n, x = - 95.73917 \dots^{\circ} + 36 0^{\circ} n

Solution steps

2 cos (x) = - 0.2

Divide both sides by

2

2 cos (x) = - 0.2

Divide both sides by

2

\frac{2 cos ( x )}{2} = \frac{- 0.2}{2}

Simplify

\frac{2 cos ( x )}{2} = \frac{- 0.2}{2}

Simplify

\frac{2 cos ( x )}{2} : cos (x)

\frac{2 cos ( x )}{2}

Divide the numbers:

\frac{2}{2} = 1

= cos (x)

Simplify

\frac{- 0.2}{2} : - 0.1

\frac{- 0.2}{2}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{0.2}{2}

Divide the numbers:

\frac{0.2}{2} = 0.1

= - 0.1

cos (x) = - 0.1

cos (x) = - 0.1

cos (x) = - 0.1

Apply trig inverse properties

cos (x) = - 0.1

General solutions for

cos (x) = - 0.1

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

x = arccos (- 0.1) + 2 πn, x = - arccos (- 0.1) + 2 πn

x = arccos (- 0.1) + 2 πn, x = - arccos (- 0.1) + 2 πn

Show solutions in decimal form

x = 1.67096 \dots + 2 πn, x = - 1.67096 \dots + 2 πn

What is the general solution for 2cos(x)=-0.2 ?
The general solution for 2cos(x)=-0.2 is x=1.67096…+2pin,x=-1.67096…+2pin