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

The general solution for cos(x)= 1/(sqrt(3)) is x=0.95531…+2pin,x=2pi-0.95531…+2pin

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

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

x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn

Radians

x = 0.95531 \dots + 6.28318 \dots n, x = 5.32786 \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 = 2 π - arccos (a) + 2 πn

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

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

Show solutions in decimal form

x = 0.95531 \dots + 2 πn, x = 2 π - 0.95531 \dots + 2 πn

sin (x) cos (x) = \frac{3}{4}, 0 \leq x \leq 2 π

2 cos^{2} (x) + sin (x) - 1 = 0, 0 \leq x < 2 π

cot (x) = - 1, 0 \leq x \leq 2 π

(2 cos (x) - 2) (2 sin (x) + 2) = 0

4 sec^{2} (x) - 3 = 0

What is the general solution for cos(x)= 1/(sqrt(3)) ?
The general solution for cos(x)= 1/(sqrt(3)) is x=0.95531…+2pin,x=2pi-0.95531…+2pin