What is the general solution for cos(x)=-1/(sqrt(3)) ?

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

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cos(x)=-1/(sqrt(3))

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

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

Radians

x = 2.18627 \dots + 6.28318 \dots n, x = - 2.18627 \dots + 6.28318 \dots n

Solution steps

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

Simplify

- \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}

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

6 - 24 cos^{2} (t) = 0

sin^{2} (x) - sin (x) = 2, 0 \leq x \leq 2 π

tan (x) = - 2, 0 \leq x \leq 2 π

7 sin (x) = 0

cos (θ) = \frac{33}{55}

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