What is the general solution for 0.25*cos(x)=-0.249 ?

The general solution for 0.25*cos(x)=-0.249 is x=3.05212…+2pin,x=-3.05212…+2pin

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0.25*cos(x)=-0.249

0.25 \cdot cos (x) = - 0.249

x = 3.05212 \dots + 2 πn, x = - 3.05212 \dots + 2 πn

Degrees

x = 174.87359 \dots^{\circ} + 36 0^{\circ} n, x = - 174.87359 \dots^{\circ} + 36 0^{\circ} n

Solution steps

0.25 cos (x) = - 0.249

Multiply both sides by

1000

0.25 cos (x) = - 0.249

To eliminate decimal points, multiply by 10 for every digit after the decimal pointThere are

3

digits to the right of the decimal point, therefore multiply by

1000

0.25 cos (x) \cdot 1000 = - 0.249 \cdot 1000

Refine

250 cos (x) = - 249

250 cos (x) = - 249

Divide both sides by

250

250 cos (x) = - 249

Divide both sides by

250

\frac{250 cos ( x )}{250} = \frac{- 249}{250}

Simplify

cos (x) = - \frac{249}{250}

cos (x) = - \frac{249}{250}

Apply trig inverse properties

cos (x) = - \frac{249}{250}

General solutions for

cos (x) = - \frac{249}{250}

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

x = arccos (- \frac{249}{250}) + 2 πn, x = - arccos (- \frac{249}{250}) + 2 πn

x = arccos (- \frac{249}{250}) + 2 πn, x = - arccos (- \frac{249}{250}) + 2 πn

Show solutions in decimal form

x = 3.05212 \dots + 2 πn, x = - 3.05212 \dots + 2 πn

What is the general solution for 0.25*cos(x)=-0.249 ?
The general solution for 0.25*cos(x)=-0.249 is x=3.05212…+2pin,x=-3.05212…+2pin