What is the general solution for sqrt(3)cos(x)+1=0 ?

The general solution for sqrt(3)cos(x)+1=0 is x=2.18627…+2pin,x=-2.18627…+2pin

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sqrt(3)cos(x)+1=0

3 cos (x) + 1 = 0

x = 2.18627 \dots + 2 πn, x = - 2.18627 \dots + 2 πn

Degrees

x = 125.26438 \dots^{\circ} + 36 0^{\circ} n, x = - 125.26438 \dots^{\circ} + 36 0^{\circ} n

Solution steps

3 cos (x) + 1 = 0

Move

1

to the right side

3 cos (x) + 1 = 0

Subtract

1

from both sides

3 cos (x) + 1 - 1 = 0 - 1

Simplify

3 cos (x) = - 1

3 cos (x) = - 1

Divide both sides by

3

3 cos (x) = - 1

Divide both sides by

3

\frac{3 cos ( x )}{3} = \frac{- 1}{3}

Simplify

\frac{3 cos ( x )}{3} = \frac{- 1}{3}

Simplify

\frac{3 cos ( x )}{3} : cos (x)

\frac{3 cos ( x )}{3}

Cancel the common factor:

3

= cos (x)

Simplify

\frac{- 1}{3} : - \frac{3}{3}

\frac{- 1}{3}

Apply the fraction rule:

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

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

cos (x) = - \frac{3}{3}

cos (x) = - \frac{3}{3}

cos (x) = - \frac{3}{3}

Apply trig inverse properties

cos (x) = - \frac{3}{3}

General solutions for

cos (x) = - \frac{3}{3}

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

x = arccos (- \frac{3}{3}) + 2 πn, x = - arccos (- \frac{3}{3}) + 2 πn

x = arccos (- \frac{3}{3}) + 2 πn, x = - arccos (- \frac{3}{3}) + 2 πn

Show solutions in decimal form

x = 2.18627 \dots + 2 πn, x = - 2.18627 \dots + 2 πn

1 = cos^{2} (x)

cos (2 θ) + 6 sin^{2} (θ) = 3

sin (\frac{x}{4}) = \frac{- 3}{2}

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

arctan (x) = 90

What is the general solution for sqrt(3)cos(x)+1=0 ?
The general solution for sqrt(3)cos(x)+1=0 is x=2.18627…+2pin,x=-2.18627…+2pin